text:
Wieferich prime
|Named after
|Arthur Wieferich
|Publication year
|Author of publication
|Wieferich, A.
|Number of known terms
|Subsequence of
|Crandall numbers[1]
Wieferich numbers[2]
Lucas-Wieferich primes[3]
near-Wieferich primes
|First terms
|1093, 3511
|Largest known term
|OEIS index
In number theory, a Wieferich prime is a prime number p such that p2 divides 2p − 1 − 1,[4] therefore connecting these primes with Fermat's little theorem, which states that every odd prime p divides 2p − 1 − 1. Wieferich primes were first described by Arthur Wieferich in 1909 in works pertaining to Fermat's last theorem, at which time both of Fermat's theorems were already well known to mathematicians.[5][6]
Since then, connections between Wieferich primes and various other topics in mathematics have been discovered, including other types of numbers and primes, such as Mersenne and Fermat numbers, specific types of pseudoprimes and some types of numbers generalized from the original definition of a Wieferich prime. Over time, those connections discovered have extended to cover more properties of certain prime numbers as well as more general subjects such as number fields and the abc conjecture.
As of October 2013[update], the only known Wieferich primes are 1093 and 3511 (sequence A001220 in OEIS).
- 1 Equivalent definitions
- 2 History and search status
- 3 Properties
- 3.1 Connection with Fermat's last theorem
- 3.2 Connection with the abc conjecture and non-Wieferich primes
- 3.3 Connection with Mersenne and Fermat primes
- 3.4 Connection with other equations
- 3.5 Binary periodicity of p−1
- 3.6 Abundancy of p−1
- 3.7 Connection with pseudoprimes
- 3.8 Connection with directed graphs
- 3.9 Properties related to number fields
- 4 Generalizations
- 5 See also
- 6 References
- 7 Further reading
- 8 External links
Equivalent definitions[edit]
The stronger version of Fermat's little theorem, which a Wieferich prime satisfies, is usually expressed as a congruence relation 2p − 1 ≡ 1 (mod p2). From the definition of the congruence relation on integers, it follows that this property is equivalent to the definition given at the beginning. Thus if a prime p satisfies this congruence, this prime divides the Fermat quotient . The following are two illustrative examples using the primes 11 and 1093:
- For p = 11, we get which is 93 and leaves a remainder of 5 after division by 11, hence 11 is not a Wieferich prime. For p = 1093, we get or 485439490310...852893958515 (302 intermediate digits omitted for clarity), which leaves a remainder of 0 after division by 1093 and thus 1093 is a Wieferich prime.
Wieferich primes can be defined by other equivalent congruences. If p is a Wieferich prime, one can multiply both sides of the congruence 2p-1 ≡ 1 (mod p2) by 2 to get 2p ≡ 2 (mod p2). Raising both sides of the congruence to the power p shows that a Wieferich prime also satisfies 2p2 ≡2p ≡ 2 (mod p2), and hence 2pk ≡ 2 (mod p2) for all k ≥ 1. The converse is also true: 2pk ≡ 2 (mod p2) for some k ≥ 1 implies that the multiplicative order of 2 modulo p2 divides gcd(pk-1,φ(p2))=p-1, that is, 2p-1 ≡ 1 (mod p2) and thus p is a Wieferich prime. This also implies that Wieferich primes can be defined as primes p such that the multiplicative orders of 2 modulo p and modulo p2 coincide: ordp2 2 = ordp 2, (By the way, ord10932 = 364, and ord35112 = 1755).
H. S. Vandiver proved that 2p-1 ≡ 1 (mod p3) if and only if .[7]:187
History and search status[edit]
In 1902, W. F. Meyer proved a theorem about solutions of the congruence ap − 1 ≡ 1 (mod pr).[8]:930 Later in that decade Arthur Wieferich showed specifically that if the first case of Fermat's last theorem has solutions for an odd prime exponent, then that prime must satisfy that congruence for a = 2 and r = 2. In other words, if there exist solutions to xp + yp + zp = 0 in integers x, y, z and p an odd prime with p ∤ xyz, then p satisfies 2p − 1 ≡ 1 (mod p2). In 1913, Bachmann examined the residues of . He asked the question when this residue vanishes and tried to find expressions for answering this question.[9]
The prime 1093 was found to be a Wieferich prime by Waldemar Meissner in 1913 and confirmed to be the only such prime below 2000. He calculated the smallest residue of for all primes p < 2000 and found this residue to be zero for t = 364 and p = 1093, thereby providing a counterexample to a conjecture by Grawe about the impossibility of the Wieferich congruence.[10] E. Haentzschel later ordered verification of the correctness of Meissners congruence via only elementary calculations.[11]:664 Inspired by an earlier work of Euler, he simplified Meissners proof by showing that 10932 | (2182 + 1) and remarked that (2182 + 1) is a factor of (2364 − 1).[12] It was also shown that it is possible to prove that 1093 is a Wieferich prime without using complex numbers contrary to the method used by Meissner,[13] although Meissner himself hinted at that he was aware of a proof without complex values.[10]:665
The prime 3511 was first found to be a Wieferich prime by N. G. W. H. Beeger in 1922[14] and another proof of it being a Wieferich prime was published in 1965 by Guy.[15] In 1960, Kravitz[16] doubled a previous record set by Fröberg[17] and in 1961 Riesel extended the search to 500000 with the aid of BESK.[18] Around 1980, Lehmer was able to reach the search limit of 6×109.[19] This limit was extended to over 2.5×1015 in 2006,[20] finally reaching 3×1015. It is now known, that if any other Wieferich primes exist, they must be greater than 6.7×1015.[21] The search for new Wieferich primes is currently performed by the distributed computing project Wieferich@Home. In December 2011, another search was started by the PrimeGrid project.[22] As of August 2014[update], PrimeGrid has extended the search limit to 1.5×1017 and continues.[23]
It has been conjectured (as for Wilson primes) that infinitely many Wieferich primes exist, and that the number of Wieferich primes below x is approximately log(log(x)), which is a heuristic result that follows from the plausible assumption that for a prime p, the (p − 1)-th degree roots of unity modulo p2 are uniformly distributed in the multiplicative group of integers modulo p2.[24]
Connection with Fermat's last theorem[edit]
The following theorem connecting Wieferich primes and Fermat's last theorem was proven by Wieferich in 1909:[25]
- Let p be prime, and let x, y, z be integers such that xp + yp + zp = 0. Furthermore, assume that p does not divide the product xyz. Then p is a Wieferich prime.
The above case (where p does not divide any of x, y or z) is commonly known as the first case of Fermat's last theorem (FLTI)[26][27] and FLTI is said to fail for a prime p, if solutions to the Fermat equation exist for that p, otherwise FLTI holds for p.[28] In 1910, Mirimanoff expanded[29] the theorem by showing that, if the preconditions of the theorem hold true for some prime p, then p2 must also divide 3p − 1 − 1. Granville and Monagan further proved that p2 must actually divide mp − 1 − 1 for every prime m ≤ 89.[30] Suzuki extended the proof to all primes m ≤ 113.[31]
Let Hp be a set of pairs of integers with 1 as their greatest common divisor, p being prime to x, y and x + y, (x + y)p-1 ≡ 1 (mod p2), (x + ξy) being the pth power of an ideal of K with ξ defined as cos 2π/p + i sin 2π/p. K = Q(ξ) is the field extension obtained by adjoining all polynomials in the algebraic number ξ to the field of rational numbers (such an extension is known as a number field or in this particular case, where ξ is a root of unity, a cyclotomic number field).[30]:332 From uniqueness of factorization of ideals in Q(ξ) it follows that if the first case of Fermat's last theorem has solutions x, y, z then p divides x+y+z and (x, y), (y, z) and (z, x) are elements of Hp.[30]:333 Granville and Monagan showed that (1, 1) ∈ Hp if and only if p is a Wieferich prime.[30]:333
Connection with the abc conjecture and non-Wieferich primes[edit]
A non-Wieferich prime is a prime p satisfying 2p − 1 ≢ 1 (mod p2). J. H. Silverman showed in 1988 that if the abc conjecture holds, then there exist infinitely many non-Wieferich primes.[32] More precisely he showed that the abc conjecture implies the existence of a constant only depending on α such that the number of non-Wieferich primes to base α with p less than or equal to a variable X is greater than log(X) as X goes to infinity.[33]:227 Numerical evidence suggests that very few of the prime numbers in a given interval are Wieferich primes. The set of Wieferich primes and the set of non-Wieferich primes, sometimes denoted by W2 and W2c respectively,[34] are complementary sets, so if one of them is shown to be finite, the other one would necessarily have to be infinite, because both are proper subsets of the set of prime numbers. It was later shown that the existence of infinitely many non-Wieferich primes already follows from a weaker version of the abc conjecture, called the ABC-(k, ε) conjecture.[35] Additionally, the existence of infinitely many non-Wieferich primes would also follow if there exist infinitely many square-free Mersenne numbers[36] as well as if there exists a real number ξ such that the set {n ∈ N : λ(2n − 1) < 2 − ξ} is of density one, where the index of composition λ(n) of an integer n is defined as and , meaning gives the product of all prime factors of n.[34]:4
Connection with Mersenne and Fermat primes[edit]
It is known that the nth Mersenne number Mn = 2n − 1 is prime only if n is prime. Fermat's little theorem implies that if p > 2 is prime, then Mp−1 (= 2p − 1 − 1) is always divisible by p. Since Mersenne numbers of prime indices Mp and Mq are co-prime,
- A prime divisor p of Mq, where q is prime, is a Wieferich prime if and only if p2 divides Mq.[37]
Thus, a Mersenne prime cannot also be a Wieferich prime. A notable open problem is to determine whether or not all Mersenne numbers of prime index are square-free. If q is prime and the Mersenne number Mq is not square-free, that is, there exists a prime p for which p2 divides Mq, then p is a Wieferich prime. Therefore, if there are only finitely many Wieferich primes, then there will be at most finitely many Mersenne numbers with prime index that are not square-free. Rotkiewicz showed a related result: if there are infinitely many square-free Mersenne numbers, then there are infinitely many non-Wieferich primes.[38]
Similarly, if p is prime and p2 divides some Fermat number Fn = 22n + 1, then p must be a Wieferich prime.[39]
In fact, if and only if there exists a natural number n and a prime p that p2 divides (where is Cyclotomic polynomial), then p is a Wieferich prime. For example, 10932 divides , 35112 divides . Mersenne and Fermat numbers are just special situations of . Thus, if 1093 and 3511 are only two Wieferich primes, then all are square-free except and (In fact, when there exists a prime p which p2 divides some , then it is a Wieferich prime); and clearly, if is a prime, then it cannot be Wieferich prime. (Notice any odd prime p divides only one and n divides p-1, and if and only if the period length of 1/p in binary is n, then p divides . Besides, if and only if p is a Wieferich prime, then the period length of 1/p and 1/p2 are the same (in binary). Otherwise, this is p times than that.)
For the primes 1093 and 3511, it was shown that neither of them is a divisor of any Mersenne number with prime index nor a divisor of any Fermat number, because 364 and 1755 are neither prime nor powers of 2.[40]
Connection with other equations[edit]
Scott and Styer showed that the equation px – 2y = d has at most one solution in positive integers (x, y), unless when p4 | 2ordp 2 – 1 if p ≢ 65 (mod 192) or unconditionally when p2 | 2ordp 2 – 1, where ordp 2 denotes the multiplicative order of 2 modulo p.[41]:215, 217–218 They also showed that a solution to the equation ±ax1 ± 2y1 = ±ax2 ± 2y2 = c must be from a specific set of equations but that this does not hold, if a is a Wieferich prime greater than 1.25 x 1015.[42]:258
Binary periodicity of p−1[edit]
Johnson observed[43] that the two known Wieferich primes are one greater than numbers with periodic binary expansions (1092 = 0100010001002=44416; 3510 = 1101101101102=66668). The Wieferich@Home project searches for Wieferich primes by testing numbers that are one greater than a number with a periodic binary expansion, but up to a "bit pseudo-length" of 3500 of the tested binary numbers generated by combination of bit strings with a bit length of up to 24 it has not found a new Wieferich prime.[44]
Abundancy of p−1[edit]
It has been noted (sequence A239875 in OEIS) that the known Wieferich primes are one greater than mutually friendly numbers (the shared abundancy index being 112/39).
Connection with pseudoprimes[edit]
It was observed that the two known Wieferich primes are the square factors of all non-square free base-2 Fermat pseudoprimes up to 25×109.[45] Later computations showed that the only repeated factors of the pseudoprimes up to 1012 are 1093 and 3511.[46] In addition, the following connection exists: Let n be a base 2 pseudoprime and p be a prime divisor of n. If , then also .[28]:378 Furthermore if p is a Wieferich prime, then p2 is a Catalan pseudoprime.[47]
Connection with directed graphs[edit]
For all primes up to 100000 L(pn+1) = L(pn) only for two cases: L(10932) = L(1093) = 364 and L(35112) = L(3511) = 1755, where m is the modulus of the doubling diagram and L(m) gives the number of vertices in the cycle of 1. The term doubling diagram refers to the directed graph with 0 and the natural numbers less than m as vertices with arrows pointing from each vertex x to vertex 2x reduced modulo m.[48]:74 It was shown, that for all odd prime numbers either L(pn+1) = p × L(pn) or L(pn+1) = L(pn).[48]:75
It was shown that and if and only if 2p − 1 ≢ 1 (mod p2) where p is an odd prime and is the fundamental discriminant of the imaginary quadratic field . Furthermore the following was shown: Let p be a Wieferich prime. If p ≡ 3 (mod 4), let be the fundamental discriminant of the imaginary quadratic field and if p ≡ 1 (mod 4), let be the fundamental discriminant of the imaginary quadratic field . Then and (χ and λ in this context denote Iwasawa invariants).[49]:27
Furthermore the following result was obtained: Let q be an odd prime number, k and p are primes such that p = 2k + 1, k ≡ 3 (mod 4), p ≡ −1 (mod q), p ≢ −1 (mod q3) and the order of q modulo k is . Assume that q divides h+, the class number of the real cyclotomic field , the cyclotomic field obtained by adjoining the sum of a p-th root of unity and its reciprocal to the field of rational numbers. Then q is a Wieferich prime.[50]:55 This also holds if the conditions p ≡ −1 (mod q) and p ≢ −1 (mod q3) are replaced by p ≡ −3 (mod q) and p ≢ −3 (mod q3) as well as when the condition p ≡ −1 (mod q) is replaced by p ≡ −5 (mod q) (in which case q is a Wall−Sun−Sun prime) and the incongruence condition replaced by p ≢ −5 (mod q3).[51]:376
Near-Wieferich primes[edit]
A prime p satisfying the congruence 2(p−1)/2 ≡ ±1 + Ap (mod p2) with small |A| is commonly called a near-Wieferich prime (sequence A195988 in OEIS).[24][52] Near-Wieferich primes with A = 0 represent Wieferich primes. Recent searches, in addition to their primary search for Wieferich primes, also tried to find near-Wieferich primes.[21][53] The following table lists all near-Wieferich primes with |A| ≤ 10 in the interval [1×109, 3×1015].[54] This search bound was reached in 2006 in a search effort by P. Carlisle, R. Crandall and M. Rodenkirch.[20][55]
|1 or −1
The sign +1 or -1 above can be easily predicted by Euler's criterion (and the second supplement to the law of quadratic reciprocity).
Dorais and Klyve[21] used a different definition of a near-Wieferich prime, defining it as a prime p with small value of where is the Fermat quotient of 2 with respect to p modulo p (the modulo operation here gives the residue with the smallest absolute value). The following table lists all primes p ≤ 6.7 × 1015 with .
The two notions of nearness are related as follows. If , then by squaring, clearly . So if had been chosen with small, then clearly is also (quite) small, and an even number. However, when is odd above, the related from before the last squaring was not "small". For example with , we have which reads extremely non-near, but after squaring this is which is a near-Wieferich by the second definition.
Base-a Wieferich primes[edit]
A Wieferich prime base a is a prime p that satisfies
- ap − 1 ≡ 1 (mod p2).[8]
Such a prime cannot divide a, since then it would also divide 1.
Bolyai showed that if p and q are primes, a is a positive integer not divisible by p and q such that ap-1 ≡ 1 (mod q), aq-1 ≡ 1 (mod p), then apq-1 ≡ 1 (mod pq). Setting p = q leads to ap2-1 ≡ 1 (mod p2).[56]:284 It was shown that ap2-1 ≡ 1 (mod p2) if and only if ap-1 ≡ 1 (mod p2).[56]:285–286
Known solutions of ap-1 ≡ 1 (mod p2) for small values of a are:[57]
a p (checked up to 5 × 1013) OEIS sequence 1 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ... (All primes) A000040 2 1093, 3511 A001220 3 11, 1006003 A014127 4 1093, 3511 5 2, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801 A123692 6 66161, 534851, 3152573 A212583 7 5, 491531 A123693 8 3, 1093, 3511 9 2, 11, 1006003 10 3, 487, 56598313 A045616 11 71 12 2693, 123653 A111027 13 2, 863, 1747591 A128667 14 29, 353, 7596952219 A234810 15 29131, 119327070011 A242741 16 1093, 3511 17 2, 3, 46021, 48947, 478225523351 A128668 18 5, 7, 37, 331, 33923, 1284043 A244260 19 3, 7, 13, 43, 137, 63061489 A090968 20 281, 46457, 9377747, 122959073 A242982 21 2 22 13, 673, 1595813, 492366587, 9809862296159 23 13, 2481757, 13703077, 15546404183, 2549536629329 A128669 24 5, 25633 25 2, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801 26 3, 5, 71, 486999673, 6695256707 27 11, 1006003 28 3, 19, 23 29 2 30 7, 160541, 94727075783
For more information, see[58][59][60] and.[61]
The smallest solutions of np-1 ≡ 1 (mod p2) are
- 2, 1093, 11, 1093, 2, 66161, 5, 3, 2, 3, 71, 2693, 2, 29, 29131, 1093, 2, 5, 3, 281, 2, 13, 13, 5, 2, 3, 11, 3, 2, 7, ......(sequence A039951 in OEIS)
Wieferich pairs[edit]
A Wieferich pair is a pair of primes p and q that satisfy
- pq − 1 ≡ 1 (mod q2) and qp − 1 ≡ 1 (mod p2)
so that a Wieferich prime p ≡ 1 (mod 4) will form such a pair (p, 2): the only known instance in this case is p = 1093. There are only 7 known Wieferich pairs.[62]
- (2, 1093), (3, 1006003), (5, 1645333507), (5, 188748146801), (83, 4871), (911, 318917), and (2903, 18787) (sequences A124121, A124122 and A126432 in OEIS)
Wieferich numbers[edit]
A Wieferich number is an odd integer w ≥ 3 satisfying the congruence 2φ(w) ≡ 1 (mod w2), where φ(·) denotes the Euler function. If Wieferich number w is prime, then it is a Wieferich prime. The first few Wieferich numbers are:
- 1093, 3279, 3511, 7651, 10533, 14209, 17555, 22953, 31599, 42627, 45643, … (sequence A077816 in OEIS)
It can be shown that if there are only finitely many Wieferich primes, then there are only finitely many Wieferich numbers. In particular, if the only Wieferich primes are 1093 and 3511, then there exist exactly 104 Wieferich numbers, which matches the number of Wieferich numbers currently known.[2]
More generally, an integer w is a Wieferich number to base a, if aφ(w) ≡ 1 (mod w2).[63]:31
Another definition specifies a Wieferich number as positive odd integer q such that q and are not coprime, where m is the multiplicative order of 2 modulo q. The first of these numbers are:[64]
As above, if Wieferich number q is prime, then it is a Wieferich prime.
Lucas-Wieferich primes[edit]
A Lucas-Wieferich prime associated with the pair of integers (P, Q) is a prime p such that Up-ε(P, Q) ≡ 0 (mod p2), where Un(P, Q) denotes the Lucas sequence of the first kind and ε equals the Legendre symbol of P2 - 4Q modulo p. All Wieferich primes are Lucas-Wieferich primes associated with the pair (3, 2).[3]:2088
Wieferich places[edit]
Let K be a global field, i.e. a number field or a function field in one variable over a finite field and let E be an elliptic curve. If v is a non-archimedean place of norm qv of K and a ∈ K, with v(a) = 0 then v(aqv-1-1) ≥ 1. v is called a Wieferich place for base a, if v(aqv-1-1) > 1, an elliptic Wieferich place for base P ∈ E, if NvP ∈ E2 and a strong elliptic Wieferich place for base P ∈ E if nvP ∈ E2, where nv is the order of P modulo v and Nv gives the number of rational points (over the residue field of v) of the reduction of E at v.[65]:206
See also[edit]
- Wolstenholme prime – another type of prime number which in the broadest sense also resulted from the study of FLT
- Table of congruences - lists other congruences satisfied by prime numbers
- PrimeGrid - primes search project
- Distributed computing
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- ^ PrimeGrid Announcement of Wieferich and Wall-Sun-Sun searches
- ^ PrimeGrid Wieferich prime search server statistics
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- ^ a b DeKoninck, J.-M.; Doyon, N. (2007), "On the set of Wieferich primes and of its complement", Annales Univ. Sci. Budapest., Sect. Comp. 27: 3–13
- ^ Broughan, K. (2006), "Relaxations of the ABC Conjecture using integer k 'th roots", New Zealand J. Math. 35 (2): 121–136
- ^ Ribenboim, P. (1979). 13 Lectures on Fermat's Last Theorem. New York: Springer. p. 154. ISBN 0-387-90432-8.
- ^ Mersenne Primes: Conjectures and Unsolved Problems
- ^ Rotkiewicz, A. (1965). "Sur les nombres de Mersenne dépourvus de diviseurs carrés et sur les nombres naturels n, tels que n2∣2n-2". Mat. Vesnik (in French) 2 (17): 78–80.
- ^ Ribenboim, Paulo (1991), The little book of big primes, New York: Springer, p. 64, ISBN 0-387-97508-X
- ^ Bray, H. G.; Warren, L. J. (1967), "On the square-freeness of Fermat and Mersenne numbers", Pacific J. Math. 22 (3): 563–564, doi:10.2140/pjm.1967.22.563, MR 0220666, Zbl 0149.28204
- ^ Scott, R.; Styer, R. (April 2004). "On px-qy=c and related three term exponential Diophantine equations with prime bases". Journal of Number Theory (Elsevier) 105 (2): 212–234. doi:10.1016/j.jnt.2003.11.008.
- ^ Scott, R.; Styer, R. (2006). "On the generalized Pillai equation ±ax±by=c". Journal of Number Theory 118 (2): 236–265. doi:10.1016/j.jnt.2005.09.001.
- ^ Wells Johnson (1977), "On the nonvanishing of Fermat quotients (mod p)", J. Reine angew. Math. 292: 196–200
- ^ Dobeš, Jan; Kureš, Miroslav (2010), "Search for Wieferich primes through the use of periodic binary strings", Serdica Journal of Computing 4: 293–300, Zbl 05896729.
- ^ Ribenboim, P. (2004), "Chapter 2. How to Recognize Whether a Natural Number is a Prime", The Little Book of Bigger Primes, New York: Springer-Verlag New York, Inc., p. 99, ISBN 0-387-20169-6 Archived at WebCite
- ^ Pinch, R. G. E. (2000). "The Pseudoprimes up to 1013". Lecture Notes in Computer Science 1838: 459–473. doi:10.1007/10722028_30.
- ^ Aebi, C.; Cairns, G. (2008). "Catalan numbers, primes and twin primes". Elemente der Mathematik 63 (4): 153–164. doi:10.4171/EM/103. Archived at WebCite
- ^ a b Ehrlich, A. (1994), "Cycles in Doubling Diagrams mod m", The Fibonacci Quarterly 32 (1): 74–78.
- ^ Byeon, D. (2006), "Class numbers, Iwasawa invariants and modular forms", Trends in Mathematics 9 (1): 25–29
- ^ Jakubec, S. (1995), "Connection between the Wieferich congruence and divisibility of h+", Acta Arithmetica 71 (1): 55–64
- ^ Jakubec, S. (1998), "On divisibility of the class number h+ of the real cyclotomic fields of prime degree l", Mathematics of Computation 67 (221): 369–398, doi:10.1090/s0025-5718-98-00916-8
- ^ Joshua Knauer; Jörg Richstein (2005), "The continuing search for Wieferich primes", Math. Comp. 74 (251): 1559–1563, doi:10.1090/S0025-5718-05-01723-0.
- ^ About project Wieferich@Home
- ^ PrimeGrid, Wieferich & near Wieferich primes p < 11e15
- ^ Ribenboim, Paulo (2000), My numbers, my friends: popular lectures on number theory, New York: Springer, pp. 213–229, ISBN 978-0-387-98911-2
- ^ a b Kiss, E.; Sándor, J. (2004). "On a congruence by János Bolyai, connected with pseudoprimes". Mathematica Pannonica 15 (2): 283–288.
- ^ Fermat Quotient at The Prime Glossary
- ^ Wieferich primes to base 1052
- ^ Wieferich primes to base 10125
- ^ Wieferich prime in prime bases up to 1000
- ^ Wieferich primes with level >= 3
- ^ Weisstein, Eric W., "Double Wieferich Prime Pair", MathWorld.
- ^ Agoh, T.; Dilcher, K.; Skula, L. (1997), "Fermat Quotients for Composite Moduli", Journal of Number Theory 66 (1): 29–50, doi:10.1006/jnth.1997.2162
- ^ Müller, H. (2009). "Über Periodenlängen und die Vermutungen von Collatz und Crandall". Mitteilungen der Mathematischen Gesellschaft in Hamburg (in German) (Mathematische Gesellschaft in Hamburg) 28: 121–130.
- ^ Voloch, J. F. (2000), "Elliptic Wieferich Primes", Journal of Number Theory 81: 205–209, doi:10.1006/jnth.1999.2471
Further reading[edit]
- Haussner, R. (1926), "Über die Kongruenzen 2p-1-1 ≡ 0 (mod p2) für die Primzahlen p=1093 und 3511", Archiv for Mathematik og Naturvidenskab (in German) 39 (5): 7, JFM 52.0141.06, DNB 363953469
- Haussner, R. (1927), "Über numerische Lösungen der Kongruenz up-1-1 ≡ 0 (mod p2)", Journal für die reine und angewandte Mathematik (Crelle's Journal). (in German) 1927 (156): 223–226, doi:10.1515/crll.1927.156.223
- Ribenboim, P. (1979), Thirteen lectures on Fermat's Last Theorem, Springer-Verlag, pp. 139, 151, ISBN 0-387-90432-8
- Guy, Richard K. (2004), Unsolved Problems in Number Theory (3rd ed.), Springer Verlag, p. 14, ISBN 0-387-20860-7
- Crandall, R. E.; Pomerance, C. (2005), Prime numbers: a computational perspective, Springer Science+Business Media, Inc., pp. 31–32, ISBN 0-387-25282-7
- Ribenboim, P. (1996), The new book of prime number records, Springer-Verlag New York, Inc., pp. 333–346, ISBN 0-387-94457-5
External links[edit]
- Weisstein, Eric W., "Wieferich prime", MathWorld.
- Fermat-/Euler-quotients (ap−1 − 1)/pk with arbitrary k
- A note on the two known Wieferich primes
- PrimeGrid's Wieferich Prime Search project page


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The San Francisco 49ers look to lock up a spot in Super Bowl XLVIII on Sunday afternoon as they face the Seattle Seahawks in the 2014 NFC Championship Game. The 49ers travel north to CenturyLink Field to face the NFC West winning Seahawks. The game kicks off at 3:30 p.m. PT, and the Seahawks are currently 3 1/2 point favorites.
This game serves as the rubber match of their season series. The Seahawks claimed the first game 29-3 up in Seattle in Week 2. The 49ers gained a small measure of revenge in Week 14 with a 19-17 win at Candlestick Park. Much changed from Week 2 to Week 14, and much has since changed for the 49ers. Michael Crabtree has almost two months worth of games under his belt, and the offense is thriving with him.
The Seahawks have claimed the last two games at CenturyLink by a combined score of 71-16. Colin Kaepernick is 0-2 up in Seattle, and given those big wins the previous two trips, it's easy to see how the narrative spins toward the Seahawks having the significant upper-hand.
And yet, this 49ers team is different than the teams we saw in Week 2 of this season, and late last season. The return of Michael Crabtree has opened up the passing game, and has the 49ers in a position to further open the run game against the Seahawks. For the first time in the Jim Harbaugh era, the 49ers have three legitimate receiving options in Michael Crabtree, Anquan Boldin and Vernon Davis. It might not seem huge to outsiders, but given that this team has rolled out run-down versions of Braylon Edwards and Randy Moss, and guys like Joe Hastings and Brett Swain as the No. 2 WR, this is kind of a big deal.
The question now is how exactly the 49ers elect to attack the Seahawks defense. The run defense is Seattle's biggest weakness, and even that is not quite so bad. Do the 49ers just attack with a steady dose of Frank Gore? Do they go after the weaker links of the Seahawks vaunted secondary? Do they take some shots against the big names? In Week 14, the 49ers avoided Richard Sherman for most of the game. I suspect we'll see something similar this week.
They'll still need to hold up against the pass rush of that incredibly deep defensive line, so we'll see how they handle the rotation of players. Do we see some no-huddle to mix things up and keep the Seahawks on their heels?
On the other side of the ball, the 49ers biggest concerns will be Marshawn Lynch. Russell Wilson could bust out with a big game, but the 49ers first job is to shut down Beast Mode. He's had more success against the 49ers than most any other running back in the league. If they can contain him, they put Russell Wilson in a position where needs to start making plays.
Russell Wilson remains a dynamic playmaker, but his team has been able to get into a position where he can play more of a game manager role. The 49ers need to keep him from getting out and scrambling, and instead force him to beat them from the pocket. He can do that, but he is more dangerous when he starts running around. Do the 49ers cut down on the blitzing, or hope they can get guys to him to put him on his back? Do they spy him with NaVorro Bowman or Patrick Willis, or do they just look for the defensive line to keep him from getting too fleet of foot?
So many questions for two teams that know each other fairly well at this point. There will be wrinkles unleashed by both coaching staffs, but as the cliche goes, it really just comes down to execution. As part of that, the team that wins the turnover battle is likely the team that emerges victorious. Colin Kaepernick and Russell Wilson can make big plays, but the one who makes more mistakes is likely the one who goes home for the offseason.
Here is a rundown of all the pertinent broadcast details, along with the final injury report, officials and more.
Game time: 3:30 p.m. (Pacific Time)
Location: CenturyLink Field, Seattle, WA
TV Channel: FOX
Announcers: Joe Buck, Troy Aikman, Pam Oliver, Erin Andrews
Radio: KGO 810 AM, The Bone 107.7 FM; 49ers Radio Network - Ted Robinson, Eric Davis; Westwood One - Kevin Kugler, James Lofton, Mark Malone; Spanish Radio KTRB 860 - Erwin Higueros, Jesus Zarate
Odds: Pick 'em
Online streaming: FOX Sports Go (Live); NFL Rewind (Not Live)
Questionable: CB Carlos Rogers (hamstring), FB Will Tukuafu (knee)
Probable: LB Navorro Bowman (wrist), LB Ahmad Brooks (illness), WR Michael Crabtree (wrist), DE Demarcus Dobbs (knee, shoulder), C Jonathan Goodwin (foot), RB Frank Gore (knee), LB Dan Skuta (foot), DT Justin Smith (shoulder)
Last time they played: 49ers won 19-17 (12/8/2013)
SB Nation blog: Field Gulls | 5 offense questions with Field Gulls | 5 defense questions with Field Gulls | 5 offense questions with Niners Nation | 5 defense questions with Niners Nation | Under-the-radar players | What has changed since Week 14
- 49ers-Seahawks predictions: What's the first play, and what should the first play actually be?
- 12 Reasons to hate the "12th Man"
- How to plan your 49ers-Seahawks NFC title game party
- Colin Kaepernick and Russell Wilson have had strikingly similar seasons
- 49ers vs. Seahawks: How things have changed since Week 14

subset: commoncrawl


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WILMINGTON, NC (WECT) – A movie filmed in Wilmington will make its world premiere at the NYC Independent Film Festival this week.
Don't Know Yet stars James Kyson (Heroes) and Lisa Goldstein (One Tree Hill). The movie will debut at the film festival on Thursday, October 17, 7:00 p.m.
Terry Linehan, a UNCW professor, wrote and directed the feature film.
The movie is about a heartbroken man looking for life's answers as he travels through North Carolina, giving rides to hitchhikers.
David Andrews (World War Z), Bill Ladd and Jane McNeill Balter (The Walking Dead) also make appearances in the flick.
You can watch the trailer for the film here.
Students from UNCW's Department of Film Studies also helped bring the script to life.
While in Wilmington, they shot on location at the Goody Goody Omelet House, Lula's Pub, and Jackson's Big Oak BBQ. They also shot scenes near Asheville.
Linehan called the movie "a love letter to the state of North Carolina."
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My doctor asked me that a few weeks back.
I've always considered myself as a person who handles stress fairly well, but my doc seemed to think I might not be handling life's pressures as well as I should.
After hearing his question, I immediately said, "What do you think about yoga?"
My doctor said that he thought that would be a perfect way to reduce stress.
Why was yoga the first thing that popped in my mind when asked about ways to reduce stress?
My aunt, Jilda Watson, is a certified yoga instructor. For years, I've heard her emphasize the positive impacts of yoga, and the relief of stress is often one of the first positives she mentions.
In the past, I've tried some "in-home" yoga, but that was only for a short time when Andrea was struggling with some back issues during pregnancy. Jilda had sent a couple of yoga DVDs home with her, and I promised to participate with her. The yoga actually did relieve some of her back pain.
After my doctor's appointment, I called Andrea and said, "we're all going to Jilda's next yoga class."
Jilda teaches a free yoga class on Mondays at the Sumiton Community Center. A couple of weeks ago, the Phillips family made our first appearance.
If we're going somewhere as a family, we are generally at least five minutes late. Our first yoga class was no exception.
As we walked in, I noticed everyone in the room turn and look. I can only imagine what was running through their minds. It was probably something like, "Oh my goodness. I came here to relieve stress and these turkeys just brought four little kids to yoga class."
We grabbed up our mats and began to participate. I've always been concerned about doing yoga in public. The few times I tried DVD yoga, the stretching and breathing seemed to awaken something inside my stomach. Without being too gross, yoga seemed to be a great way to alleviate trapped gas. That was my main concern for trying yoga in public.
To my surprise, that problem never happened during my first class.
Also to my surprise, my children absolutely loved the class.
Breeze and Daisy, ages 7 and 5, did their best to emulate their great aunt. Both of them did a good job.
The surprise superstar of the class was Stone, our 10-year-old son. He performed each stretch flawlessly and said he loved the class. Stone even asked if we could incorporate yoga into some of our sports team practices.
I honestly thought the trouble child would be Joy, our 1-year-old.
Who brings a 1-year-old to a yoga class?
I know. It sounds pretty stupid, but she actually enjoyed herself and wasn't much trouble. She crawled around and giggled for most of the time.
The relaxation point of the class — or nap time as I call it — was the biggest shocker of the first class for me. During that part of class, everything gets quiet and soft music plays. Jilda, in a soft, quiet voice, does a great job of talking you into a relaxed state. Some of what she says is kind of wacky, like telling you to imagine a beautiful, red rose on your chest, but it works. I was very relaxed and could have probably fallen asleep. All I needed was a blanket, which was offered to me, but I just thought it was too strange to cuddle up under a blanket amidst a bunch of strangers.
For the past two weeks, we've made it to yoga class and had a great time. Luckily, my worst fear still hasn't struck, but I am going to try to stay at the back of the class in case it does. I also tried a blanket during the second class, and I've got to admit, relaxation time was pretty awesome. I almost fell asleep.
If you're looking for a way to get a little extra exercise and relieve some stress, give the free yoga class at the Sumiton Community Center a try. It's each Monday night, and try to be there by 7 p.m., and I'll see you about 7:05.
James Phillips is Editor of the Daily Mountain Eagle. He can be reached at 205-221-2840 or email@example.com.


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I am a rebel user and love indoor soft light style portraits, using window light etc.
I use a 50mm 1.4 + Samyang 85mm 1.4 MF. Both are superb.
I wanted to purchase something longer with AF (using the samyang MF requires a tripod) than can be used for candid head shoulder shots, both indoors and out no flash.
I was looking at:
canon 85mm 1.8
canon 100 2
Canon 100mm macro L IS 2.8
Canon 135mm f/2
Obviously the price range of the first 2 options is opx 1/3 then the second two.
Any of our seasoned users can give me some input ?
100mm F/2 if your strapped for cash, But preferably the 135L if you can.
The 135L is just a magic black tube with AF. On crop bodies, You'll have to deal with a minimum shutter speed of 1/200th or faster. This can be a problem because you can't bump the ISO too high on Canon Crop bodies before it look gahh. On the same token, the extra lens sharpness will allow you to be more aggressive with the NR w/o losing too much detail.
The 135L was my first L grade lens. I will never depart from it, unless a 135mm F/1.8L IS USM is released. Then, I'd part with it.


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The No. 2 Miami Hurricanes made just 6-of-28 shot attempts on their way to a 16-point first half against the No. 3 Marquette Golden Eagles in the Sweet 16 of the 2013 NCAA Tournament on Thursday.
For more on this game, head over to State of the U and Anonymous Eagle.
Miami continued to hoist up 3-pointers despite making just one of their 12 attempts, leading to this rather depressing graphic depicting the Hurricanes' effort (via @ESPNStatsInfo on Twitter):
Miami scored only 16 first-half points against Marquette. Their shot chart is pretty rough ... yfrog.com/5frnp3j— ESPN Stats & Info (@ESPNStatsInfo) March 29, 2013
The Golden Eagles entered the break with a 28-16 lead by holding the 'Canes to a 21.8-percent clip from the field while hitting 44.4 percent of their own shot attempts.
More in College Basketball:
• 16 things you should know about the Sweet 16
• Get ready for an all-B1G Final Four
• Bill Connelly: Here's how FGCU beats Florida
• Sweet 16 power rankings: Cards still on top
• Printable bracket for March Madness


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National Violent Death Reporting System
In 2002 the Centers for Disease Control and Prevention (CDC) began implementing the National Violent Death Reporting System (NVDRS). NVDRS is a state-based surveillance system that links data from law enforcement, coroners and medical examiners, vital statistics, and crime laboratories to assist each participating state in designing and implementing tailored prevention and intervention efforts. NVDRS provides data on violence trends at national and regional levels; each state can access all of these important data elements from one central database.
States that are funded for NVDRS operate under a cooperative agreement with CDC to whom all violent deaths are voluntarily reported. NVDRS funded six states initially. In 2009 CDC received funding to expand the system to a total of 18 states. The goal is to include eventually all 50 states, all U.S. territories, and the District of Columbia in the system.
NVDRS State Profiles
- Alaska(Data years 2003-2010 available)
- Colorado(Data years 2004-2010 available)
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Santa Cruz Mountains wineries are bringing their tasting rooms to the Harbor Village Shops at the Oceano Hotel in Half Moon Bay. Date and time to be determined. Wine lovers can sip wine from 15 Santa Cruz Mountains wineries, including wineries not usually open to the public. Enjoy live music and food for sale by local restaurants. This event is like a Farmer's Market, you can try it and then buy it if you like it. This will be a…Find out more »
Join us for an exclusive winemaker dinner and tasting with the Cabernet producers of the Santa Cruz Mountains. This event is not to be missed! Cabernet lovers will sip, sample and enjoy an array of new releases as well as be able to bid on exclusive hard to find library wines.Find out more »
NOVEMBER 2014 PASSPORT DAYS Passport Days to the Santa Cruz Mountains was introduced in 1993, by the Winegrowers of the Santa Cruz Mountains. Four times a year the winegrowing community of the Santa Cruz Mountains comes together to celebrate the generations of farmers, vintners and families that are the roots of the Santa Cruz Mountains wine region. Over the last 20 years the event has become a beloved tradition among wine lovers who enjoy wines produced by our legendary, artisan…Find out more »
Enjoy three days in the Santa Cruz Mountains by participating in Pinot Paradise! This three day event invites you to come learn, explore and taste the Pinot Noirs produced from our legendary winemakers.Find out more »


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Chitale Bandhu, a 62-year-old institution, sells 3,000 kilos of its famed bhakarwadis everyday.
Every city has a sweet tooth. Chennai has jangiri and mysore pak, Kolkata gets high on rosogollas, Delhi gorges on rabdi jalebi and Pune is famous for its pedhas. One place that has been whetting Pune's appetite for sweets and savouries (namkeen) over 62 years is the famous Chitale Bandhu.
Chitale generates a more profound recall value for its Bhakarwadi, a crisp and spicy Maharashtrian snack which has a long shelf life.
Set up in 1950 in a 500 sq. ft. shop, Chitale Bandhu has had a successful journey with two company-owned shops in the city's vibrant localities of Bajirao Road and Deccan Gymkhana. Besides, there are eleven franchises spread across the city through which the brand sells.
The Chitale brand also exports its namkeen, especially bhakarwadi, to the US, Israel and Singapore.
With an annual turnover of about Rs 200 crore and 2,500 to 3,000 customers shopping on average a day across two shops, the Chitale brand has been a part of celebration for many of the city's households.
The menu at Chitale is as rich as its heritage with over 60 different sweets and 40 namkeen. However, it is their bhakarwadi which sell like hot cakes. Three attendants serve the customers on the bhakarwadi counter, where it is often normal to find queues.
Started in 1970, bhakarwadi was an instant hit. "In 1972, we installed machines to give shape and size to bhakarwadi as the queues started increasing," says Srikrushna Chitale, proprietor of the Bajirao Road branch.
Today the bhakarwadi sells about 3,000 kilos a day. In the early 1970s, it was about 300 kilos. People are very critical to Chitale's business, which boasts a 300-strong workforce.
The success of the Chitale brand is that it has kept pace with the times and with people's aspirations. Be it introducing machines to sort and cut different products or be it the computerised billing system that the shop introduced in 1985, the Chitales have ensured that they remain in vogue even as they try and maintain their traditional class. "Even as we mechanised there was no question of compromising on quality. It was the first time that any mithai shop introduced computerised billing in Pune," adds Chitale proudly as he alternates between this interview and signing vouchers every five minutes.
The family, which also sells the popular Chitale milk separately, works on a joint-divide concept.
"We are a joint family… but we are a joint-divide family. In joint families, it happens that internal household problems come into the business. That is something my grandfather, B.G. Chitale, saw really early. He told us, 'Don't live together.' He said everybody should have their own house," says the younger Chitale. "We are all living in nuclear families … but live close to each other. Any business problem, we all sort it out together."
The women of the household advise on product development and product innovation. "Ours is a kitchen-driven business … so their expertise always comes in handy," he says.
Both shops have a modern customer management process. This is evident when the security at the gate hands a grey plastic card to the customer at the entrance. This is a programmed card which can store up to 40 products in its memory. So, a customer buying at different counters can simply hand over his card to the attendant who enters the quantity purchased. This, when presented at the billing counter, eases the bill payment process and saves time.
It is, however, not a sweet run for the Bandhus always. The business has its own set of challenges. The products sold are highly perishable in nature and require robust inventory management. "Everyday we monitor our production. If yesterday there was rain, we just curtail the production because the previous day's production might continue today. We manage demand and supply on daily basis," he adds.
Other than for milk, which gets supplied through his uncle's factory in Bhilawdi near Sangli, getting good raw materials is a challenge. "We have a tough time in ensuring that we procure good quality raw material. Pesticides and fertilisers have also adversely impacted the quality of raw materials," he rues.
Inflation does not seem to have dented customer's propensity to throng Chitale Bandhu, however. "Our business, on an average grows at 10 per cent and typical margins are 13-14 per cent. There have been no changes. Five years ago we used to sell 10 per cent of cashew mithai than what we sell now. Cashew prices have shot up but demand has also gone up. We feel people have a lot of money."
However, consumption of sweets and savouries is not restricted to festivals. "People consume mithai even without any occasion. It might not be as much in the North. Here, there are very few people who consume one kilo but there are many who buy a quarter of a kilo," says SR.
He learnt much of his business by observation.
"When I was in VII standard, I used to sit in the shop and observe. It was very easy for us as we stayed above the shop when we started. But my son has to acquire the knowledge after graduation. He has to go to the factory," he adds.
The Chitales do not plan to professionalise the company as they feel it robs them of their independence.
"We do not even want to go private (limited) because it takes away certain executive powers that might be required to run our business successfully. The young people do not get enough of a free hand to run the business then," he says.


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The Jacksonville University women's soccer team lost in conference play for the first time Friday night, falling 1-0 to Mercer. The Dolphins had previously been unbeaten in their last six games.
JU could not muster up much of an offensive attack as the Dolphins only managed to record six shots and only one of those was on goal. The Bears outshot Jacksonville 15-6.
The game would remain scoreless after the first half, but that would quickly change only minutes into the second period. In the 50th minute, Mercer's Washida Blackman corralled a rebound Lauren Gassie and directed the ball into the back of the net for the game's only score.
No player on the Dolphin roster was able to tally more than one shot in the worst offensive performance for Jacksonville all season.
"We were not ready to play tonight," said Dolphin head coach Brian Copham. "We did not compete to the level that we know we are capable of. We ran up against a good team and have to be better prepared for the challenge in the future. We are looking forward to getting back out on Sunday and playing like we know we can."
The Dolphins (6-5-3, 3-1-2) will look to rebound from the loss as they take on Kennesaw State Sunday at 1:00 p.m.


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This month we look at Seagate hard drive announcements; Mandriva's Gdium netbook; new Red Hat solutions; JasperForge v2; AMD Linux drivers; and Gnome Linux on Garmin's Nuvi 880, 860, and 5000 navigation devices.
Professional users are always searching for an edge. Whether you work with Linux as a webmaster, programmer, system administrator, or security consultant, you know the best solution depends on finding the right tool for the job. We thought you might be interested in the following new products and updates.
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Knoppix 7.4 Released
Klaus Knopper announces the latest version of his iconic Live Linux system.
PHP Attack Puts WordPress and Drupal at Risk
All websites that use these popular CMS tools could be vulnerable to denial of service attacks if users don't install the updates.
Heartbleed Bleeds On
According to a report, many potential victims of the Heartbleed attack have patched their systems, but few have cleaned up the crime scene to protect themselves from the effects of a previous intrusion.
Drone Brain Goes Open Source
DARPA and NICTA release the code for the ultra-secure microkernel system used in aerial drones.
Password Management Services Vulnerable to Attack
Should you trust an online service to store your online passwords?
New Raspberry Pi Adds Two USB Ports
New B+ board lets you build cool things without the complication of a powered USB hub.
Microsoft Grabs No-IP.com Domains
Redmond rushes in to root out alleged malware haven.
Firefox Steps into 3D
New initiative will bring futuristic virtual reality effects to the web surfing experience.
New Trojan Targets Online Banking
Dyreza malware launches a man-in-the-middle attack that compromises SSL.
HP Rolls Out Massive Cloud Network
New cloud combines worldwide access with local attention to data security.


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In her role as an animal fairy, Fawn is responsible for teaching baby birds to fly, painting spots on ladybugs, and coaxing butterflies to hatch. Here's a fun and simple way for your child to try her hand at a little magical metamorphosis: transforming scraps of colorful paper into a collection of pretty little butterflies to adorn a houseplant or string into a mini mobile.
You'll need:
- Scissors
- Ruler
- Scrapbook paper
- Pipe cleaners
|1. For each butterfly, cut two 2 1/2-inch squares from scrapbook paper. Trim the left and right sides of the squares to round them, as shown.
2. Accordion-fold each of the squares to create two sets of wings.
|3. For the butterfly's body, cut a pipe cleaner in half. Fold one of the halves into a V-shape, as shown, and twist the ends together a few times just above the bend to create an abdomen (it should be about an inch long).
4. Sandwich both sets of wings between the pipe cleaner ends above the abdomen, and twist the ends a couple more times to hold them snugly in place.
5. Use your fingers to pull the wings open a bit, and then curl the tips of the pipe cleaner to shape antennae.
More Disney Fairy Crafts & Recipes
Get to know Tinker Bell and all of her friends at the official Disney Fairies site!


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Author of
Home Workshops & Speaking &... Anticonventional Thinking Creativity Articles Report 103 eJournal Books About Contact
I can help you & your team think more creatively & your organisation innovate more effectively!
I have worked with organisations around the world, teaching anticonventional thinking (ACT) as well as helping innovation directors and managers improve their initiatives to focus on innovation rather than idea generation. I could help you too! Get in touch or check out my services for you.
Say No to Brainstorming!
Have you participated in, or perhaps run, brainstorming sessions only to be disappointed with the results? Do you find that brainstorms result in dozens of trivial ideas, few truly creative ideas and no implementation? If so, you are not alone! Traditional brainstorms have been proven to be an ineffective method for generating creative ideas!
Want a better approach? Try anticonventional thinking (ACT) which is based on the science of creativity and modelled after the way artists, writers, composers and other creative people collaborate on projects.
The Web's Longest Running Creativity & Innovation Resource - Since 1996!
Whether you are an innovation director seeking resources to help you manage innovation better or a CEO wanting to understand the truth about corporate creativity and innovation, you have come to the right place. On the web site, you will find over 100 articles on creativity, innovation and anticonventional thinking.
Read this popular article - "Seven Things the Competent Innovation Manager Should Know"
Learn about Anticonventional Thinking and why it is way better than brainstorming!
My Latest Creativity & Innovation Articles
Consultant, Innovate Thyself
Creative Dishonesty
Podcast Interview
ACT 3.0 White Paper
Creativity and Booze
Visualise It
Realistic Expectation of Implementation
I spoke about anticonventional thinking (ACT) at TEDxULB (Université libre de Bruxelles) on 26 June. They described my talk as "the future of creative idea generation."
World Innovation Convention
I am leading a Cosmic Creativity workshop at the World Innovation Convention in Cannes in November.
Tablelands Innovation Expo
I spoke on Inner Mind Creativity (aka Cosmic Creativity) at the Tablelands Innovation Expo in Malanda, Queensland, Australia on 16 May.
Radio Interview
Jim Beach interviewed me for his School for Startups show on Liberty Express radio. You can listen to it here (second interview).
Entrepreneur Summit in Mumbai
I spoke about cosmic creativity, anticonventional thinking and implementing ideas at The Entrepreneurship Summit 2014 in Mumbai.
While walking around the IIT campus (where the summit was held), I was surprised to see a banner with my face on it (above)!
Innovation Blogger of the Year
I was voted the Innovation Blogger of the year for 2013, which was a surprise as, strictly speaking, I don't write a blog! I write Report 103, a popular eJournal and regular articles on creativity -- which are often republished by other blogs.
My Creative Work
You can find examples of my creative writing, humour and artwork as well as info about my science fiction humour novel, The Insane Journey, at ungodly.com.
j p b . c o m
Erps-Kwerps (near Leuven & Brussels) Belgium
©1996-2014 Jeffrey Baumgartner


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Tosha Rooks
Second Place
Rooks' winning program, "Whole Village Saturday Academy," is designed to educate parents while also educating the students at Clara J. Peck Elementary School. Nearly half of the students at the school are not native English speakers; once they leave school, little English is often spoken at home. Parents are a child's first teacher and want to help their children thrive in school and in the community. The program seeks to help build the relationship between home and school to help students succeed. Objectives for the program include: teaching students strong English language skills; providing tutorial services in reading, math and science; offering parents a place to learn English in a comfortable and nonjudgmental environment; and helping parents interact and assist their children with homework and school projects without frustration. Students and parents participate in the program on Saturdays throughout the year where they work with a school translator, ESL instructor and high school volunteer. The Saturday sessions often become family events where other family members who want to improve their English skills also attend. Rooks is excited that entire families want to improve their communication.


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7" Google Android 4.0 HD TouchScreen Tablet 4GB Capacitive w/ Camera & Wi-Fi - Available in Black or White (Factory Reconditioned)
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Just when you thought you couldn't gleam the cube any harder, along comes the 7" Android 4.0 Tablet, enabling you to live your life far beyond your wildest imagination. Featuring all the glorious capabilities of Android version 4.0, including web browsing, video viewing, music playing, and whatever you can possibly pray for lies waiting in the thousands of apps in the Android marketplace. This amazing tablet ensures that staying connected to your friends, news, and favorite sites is just a touch away. Packed with a 1.3 megapixel camera and 4 GB of storage, the 7" Android 4.0 Tablet is the perfect device for rebels and dreamers of all ages put off by the price tag and design stranglehold certain other personal tablet brands have on the consumer marketplace. Up, up, and away!Learn More
Samsung WEP460 Replacement Bluetooth Ear Hooks (5 Pack) - Clear
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Lost an ear hook? Need a spare (or several) without purchasing another headset? Look no further. The Samsung WEP460 Replacement Bluetooth Ear Hooks (5 Pack) is the perfect companion to your Samsung WEP460 Bluetooth headset. Just attach it to your WEP460 and you've got additional wearing support in seconds. Make your hands-free, on-the-go lifestyle a little more secure with the Samsung WEP460 Replacement Bluetooth Ear Hooks (5 Pack).Learn More
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- F22mm lens
- Mini-tripod and carrying case included


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CATEGORIES Action, Drama, Universal, Home Entertainment, Features, CinematicalThat other Jake Gyllenhaal movie, Jarhead, has somewhat unexpectedly faded into the background as awards season peaks (though it spent last weekend at the top of the British box office, so at least people are still seeing it). Universal this week is trying to correct our collective amnesia by revealing the details of a pretty nice pair of DVD releases, due out on March 7.
Though of course there is a two disc "collector's edition" coming (more on that in a second), even the single-disc version is cool enough to labeled "special," and it really is packed with features. The single disc includes a pair of commentaries (one by director Sam Mendes, and the other by the film's writers) as well as deleted scenes and new interviews, both of which also offer optional commentary tracks. The collector's edition, meanwhile, shares all the features of the single-disc release, but also includes a disc full of additional, very vague extras. If you know what "Jarhead diaries" and "Semper Fi: Life After The Corps" are, perhaps you'll be excited by their presence, and thrilled by the fact that both include introductions by people like Mendes, and the real Anthony Swofford. If, however, you're like me and are suspicious of paying a lot for features that could be pretty much anything, it might be wise to save money and just get the cheaper SE.


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|Per night
|$175 - $200
|Per week
|$1,000 - $1,250
Home has A/C units only - no central air. Internet access.
Anna Astarb
|Oct 15 2014
|Oct 31 2014
|2 nights
|Nov 01 2014
|Nov 30 2014
|full period
|Nov 22 2014
|Nov 26 2014
|3 nights
|Dec 01 2014
|Jan 03 2015
|full period
|Jan 03 2015
|Feb 01 2015
|full period
|Feb 01 2015
|May 01 2015
|May 02 2015
|May 06 2015
|3 nights
|May 25 2015
|May 31 2015
|2 nights
|Check In: 3 p.m. Check Out: 10 a.m.
|Lodging tax: 0.00
|Deposits: Security Deposit required within 48 hours of requesting reservation to hold rental. Security deposit is one / half of total stay by night or be week. $50.00 per pet non-refundable is required with security deposit. Final rental balance due 21 days prior to reservation date. Canceling after rental balance is received will result in forfeiture of all monies received to include deposits.
|Payment Options: Personal Check, PayPal
|Other Fees: Cleaning fee of $40 for two night stay and $50.00 for three night stay. Weekly cleaning fee of $85.00. Monthly rental requires additional cleaning fee to be determined. Utilites for rental months of one or more will be additional to the monthly rental rate.Renters must provide own linens, towels, paper products to include toilet paper, paper towels, trash bags etc. 3% pay pal fees.
Brenda Conrad Bailey
Berkeley Springs, WV
February 18, 2013
The house is exactly what they describe and the pictures are perfect. Owner is very nice to work with. Very clean. Plenty of space for our family. If you plan on cooking alot, bring some of your own pots/pans and other essentials. I am sure to go back and refer to my friends/family.
Theresa Williams
October 11, 2011
We couldn't have asked for a better location in Massanutten, it close to everything. We really enjoyed our stay, although wish we would have had more time to relax and enjoy the house, but we wanted to do and see all that we could so craming in all that in 5 days & 4 nights didn't leave alot of time for the house. However the house was everything that was describe. And watch out Deer are everywhere....they were just beautiful!
Deborah Roles
Virginia Beach, Va USA
August 31, 2011
We were not planning a trip to the mountains until the last minute when my family and I needed a safe place away from the hurricane. I called that morning looking for a house and the lady I spoken to was so nice and efficient. In less then ten minutes she found me a house and gave me all the instructions I needed to start my trip. The house was wonderful!! Very clean, beautiful views, comfy beds, and the only thing I had to bring is my clothes and food. The house was well stock on everything even down to a cork screw opener for my bottle of wine. I can't wait to get back and this time it will be longer then two nights. I really enjoyed my stay, thank you.
Jim Firaben
Bristow, VA
August 3, 2011
This is a very nice place close to everything in Massanutten. The owner was easy to deal with and stayed in touch. We enjoyed our stay.
Gail Montgomery
Beckley, WV
April 28, 2011
Unfortunately, after I left my initial rave reviews, the owner is illegally trying to keep our $200.00 security deposit, stating we didn't clean enough when her cleaning lady found snack crumbs UNDER the couch CUSHION and porch dust was found inside the front door! We paid a cleaning fee and owner is keeping entire deposit for reasons that are untrue. Now we have to file a civil suit. Renters beware!
Gail Montgomery
Oak Hill, WV
April 22, 2011
House is fantastic. The furniture was really comfortable. Very clean just as others described. Perfect location to water park, same distance as the resort condos. Nice yard, nestled in a quiet court, great neighbors. We will definitely plan a return trip! We had everything we needed already equipped in the house. Great deck, too!
Jocelyn Kanner
Loudoun, VA
January 4, 2011
Nice place to rent for the price and that allows pets. We had a good time!
Robin Gibson
Fairfax Va
December 31, 2010
My family and I enjoyed this great A frame house during the holiday season. The house is located within the resort and very easy access to all the local activities.
stephens city, va
October 31, 2010
House was dirty when we arrived. Dead bugs all over and the basement is so moldy it is unusable. Furniture all smells like animals and dirty. Mold and water damage on ceilings. Stair railings insecure and unsafe. I was emailed at 9:30am on my departure date asking me when I was planning on checking out. I signed a contract to be checked out by 11am and did not like the intimidation of the homeowner to leave. It is an ok place to stay for a night but bring your own everything. I wouldn't rent this place again.
Carol Simpson
Halifax, PA USA
August 10, 2010
My husband and I, along with another couple stayed over the 4th of July weekend. The house is very cozy and we thoroughly enjoyed the hot tub on the back deck. Everything you need is there, including the towels! Amanda (owner) was gracious enough to allow early check-in/late check-out and we stayed an extra day! We have already booked this time next year!
Stafford, VA
December 29, 2009
We wanted a vacation type house that would "fit" our family and our price range and this house was it! The kids, the adults and even the dogs loved it! It's a cozy home away from home. We'd love to come back and stay longer!
not happy
richmond, va
November 4, 2009
Since this will not make your web site I should use some very harsh language. I can't beleive the way you do business. Setting people up for failure with that thick book of rules you know half the people won't read. With you srceening every review I believe none of them. At least I know the process next time. I don't need to go into whats wrong with the place you already know.
Richmond, Virginia
November 4, 2009
Linen and pillows are stained and old, Chalet needs many repairs and renovations. Owner is extremely difficult to work with, will nickel and dime your deposit down for petty, and ridiculous charges. Communication between you and owner is very strange, not dealing with a full deck... stay at your own risk!!
E. Prufer
October 12, 2009
We, a family of four, stayed for a month and made this our home away from home. It has all necessary amenities and plenty of space. We enjoyed the quiet nature around and cooking on the gas grill outside!
Haymarket, Virginia
September 19, 2009
We had a great time. We are 3 senior golfers - we cooked out on the grill every evening. The place was very clean and comfortable and there are plenty of golf courses in the area Thanks.
Diane Heglar
Kure Beach NC
February 11, 2009
WE absolutely loved it. The entire resort was extremely family friendly. We loved to tube and the staff was GREAT. The waterpark was also fantastic. Our condo was clean and beautiful.
MJ Swartz
December 24, 2007
Very nice house at an affordable rate. Only needed one night's stay and was able to relax. Close to waterpark and ski slopes, quiet cul-de-sac. Clean an roomy with a large deck.
The place was fantastic. Gayton Baptist Church, 13501 North Gayton Road, Richmond, Virginia 23233
Great house for a great price.


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The National Weather Service has issued a lake effect snow watch for the region, warning that the eastern suburbs of Cleveland -- including Solon -- could receive as much as two feet of snow between Sunday evening and Wednesday morning.
The snow will be caused by an arctic airmass that is moving into the area.
Its cold air combined with the low pressure across the Great lakes will allow for the possibility of persistent lake effect snow across Northeast Ohio and Northwest Pennsylvania.
The snow could begin as early as Sunday evening, but it's expected to be at its worst from Monday afternoon through much of Tuesday.
The snow will also be paired with a drop in temperatures. Thermometers are expected to dip to between 4 and 20 F during through Wednesday.
Finally, a wind advisory has been issued for Sunday morning.
Wind are expected to be between 31 and 39 mph with gusts reaching between 46 and 57 mph until 7 a.m. Sunday.
Winds this fast can cause property damage. Let us know of any downed power lines, trees, closed roads or the like in Solon and we'll update the story.


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Have a SmasHits account? We've already copied all your playlists, so everything is ready. Log in with the same email and password you've always used at SmasHits.com.
Log In NowStart Listening
Traveling with the Pros Pres MeetBy By Kkomal Seth & Gautam SethMahesh Bhupathi and Bikram Saluja at Traveling With The Pros Press Meet.


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Expired Property Listing
This property is disabled.
"Paradise" Winter Special $299/wk $750/Month** Total in Panama City Beach
- bedrooms 1
- baths 1
- sleeps 4
- pool yes
- hot tub no
- pets allowed no
- type Condo
- community Pirates Cove Inlet
rates (USD)
/ week
$ 1,000 - $ 1,600 / month
vacation rental description
Looking for a great place at an incredible rate? Stop searching, you've found it. Fully refurbished late June 2011 "Paradise" is a wonderful efficiency that has everything you need for the perfect beach vacation that won't break the bank. Fully stocked kitchen, impeccably clean full bath, brand new bedroom with all new bedding, new washer & dryer, tv's all located across the street from over 100 public beach access points. Centrally located to restaurants, shops & countless activities around Panama City Beach, Pier Park, Beaches of So Wal (30A), and Destin.
Pirates Cove is a quiet, friendly beach community with miles of bicycle paths, high coastal dunes and calm lakes just off Beach Front Rd. The road meanders along the Gulf and presents one of the best developed and unspoiled coastlines on the Gulf.
So come visit where the emerald waters meet sugary, white sand beaches and the warm salt air offers true vacation bliss. No matter what the perfect vacation is to you, escape the madness that is your everyday life.
Call to book your dates now as this affordable gem will book up fast.
condo rental amenities
For the cook: This modern kitchen is equipped with state-of-the-art appliances. Enjoy the electric fondue set and plates for a unique dining experience. Also equipped with blender, toaster oven, Pottery Barn placesettings for 12, non-stick cookware, crab pot, tons of kitchen gadgets and plenty of storage. Dine al-fresco on the back porch overlooking the pool.
Enjoy the pool: Not one but two wonderful pools to cool down and relax. Complete with tiki umbrellas, tables and chairs.
Beach Lovers: This is why you're here. Bring your drinks, blankets and chairs for a wonderfully fun day at what many believe to be the best beaches in the Country. Over 100 public beach access points starting just across the street complete with free parking.
activities and attractions in Panama City Beach Gulf Coast North
Pier Park/Rosemary Beach/Seaside/Silver Sands Outlet Mall/Destin/Panama City it's all centrally located.
vacation rental rates
Spring/Summer/Fall $500/week $1600/month
Winter $350/week $1000/month


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Lola Shopping Tote 4 4
great bag received this as a present. really like the pattern. flat bottom makes it stand up and not fall over. size is just right. August 21, 2014
better than I'd imagined Actually was just expecting a better than average shopping bag, but very nice strap and material--colors too-- creates a pretty and casual multipurpose bag ...combines functions of purse and bag if necessary. Nice! April 10, 2014
Great tote Even better than I expected. The Berries and Vine print looks even better in person than it does online. The bag has a great feel to it- soft to the touch and durable. I'm so happy with it, I ordered another one in Zinnia! March 30, 2014
More sturdy than expected This tote is much more sturdy than expected, with really great construction, straps; I like the bigger tote for it's added details, but wanted something not quite so large overall. Unfortunately, there is no zipper. It REALLY needs a zipper, but I'll keep it and hope articles won't slide down the aisle on the plane by tying the straps and placing it sidewaysl! February 8, 2014
1-4 of 4
Product:30387-Lola Shopping Tote


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Most popular at the top
The Value of LifeTaylor and Francis 2006; US$ 43.95
First Published in 1985. Routledge is an imprint of Taylor & Francis, an informa company. more...
The Social Work BusinessTaylor and Francis 2002; US$ 57.95
This book gives a comprehensive picture of social work in its new guise as a quasi-public enterprise, and is an invaluable resource for social work and social policy students, practice teachers, trainers and managers. more...
Early Language DevelopmentTaylor and Francis 2002; US$ 37.50
Language is of central importance in children's education and development, so providing help for the child suspected of having language difficulties is clearly of vital concern. Providing such help, or advising a teacher or parent on how best to proceed is, however, far from straightforward. Early Language Development draws together in a single volume... more...
On CloningTaylor and Francis 2004; US$ 26.95
John Harris presents an informed defence of human cloning, carefully exposing the rhetorical and highly dubious arguments against it. He shows that far from ending the diversity of human life, cloning has the power to improve and heal human life. more...
Enhancing EvolutionPrinceton University Press 2007; US$ 27.95
Decisive biotechnological interventions in the lottery of human life--to enhance our bodies and brains and perhaps irreversibly change our genetic makeup--have been widely rejected as unethical and undesirable, and have often met with extreme hostility. But in Enhancing Evolution , leading bioethicist John Harris dismantles objections to genetic... more...
Enhancing EvolutionPrinceton University Press 2010; US$ 24.95
In Enhancing Evolution , leading bioethicist John Harris dismantles objections to genetic engineering, stem-cell research, designer babies, and cloning and makes an ethical case for biotechnology that is both forthright and rigorous. Human enhancement, Harris argues, is a good thing--good morally, good for individuals, good as social policy, and... more...
Hail! Hail! Rock'n'RollLittle, Brown Book Group 2010; US$ 30.80
Want to learn how to play guitar in two pages? Ever wondered what goes into Marilyn Manson?s backstage rider? Or who wrote the worst rhyming couplet in the history of rock? John Harris?s Hail! Hail! Rock?n?Roll is the ultimate guide to what Spinal Tap called ?the majesty of rock, the mystery of roll?. Gloriously irreverent, it is also satisfyingly... more...
Hail! Hail! Rock'n'RollLittle, Brown Book Group 2010; Not Available
Want to learn how to play guitar in two pages? Ever wondered what goes into Marilyn Manson?s backstage rider? Or who wrote the worst rhyming couplet in the history of rock? John Harris?s Hail! Hail! Rock?n?Roll is the ultimate guide to what Spinal Tap called ?the majesty of rock, the mystery of roll?. Gloriously irreverent, it is also satisfyingly... more...
Why I'm Right. . .Biteback Publishing 2011; US$ 13.11
For a real insight into the bizarre circus that is the Westminster village, look no further... For two and a half years, Tom Harris used his And Another Thing... blog to dish the dirt on the reality of life as an MP. From defending politicians to dissecting Doctor Who, from how to survive a zombie holocaust to what to do when Gordon Brown forgets... more...
The Dark Side of the MoonDa Capo Press 2006; US$ 16.99
Harris's book is an indispensable, exciting read for anyone who's ever wanted to fully understand this enduring, mystifying album. ( American Songwriter ) more...


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Gemini suit hangers with locking bars in a natural finish are a must-have for any type of business professionals or anyone that owns professional clothes. Save money by protecting your expensive suits with Gemini concave suit hangers. Built out of solid wood, the Gemini suit hangers can handle the weight of a full suit without failing. The locking bar is great for hanging pants, ties, and accessories, and the design allows you to unlatch one side to easily remove or add items. The concave shape prevents wrinkles and damage to seams by following the natural lines of shirts and jackets. The sleek natural finish protects fabric from snagging on rough edges and look beautiful in any closet. Every box has 50 hangers. Also available in a light walnut finish.
Locking bottom bar that detaches for easy access Metal hooks made of durable materials secure bar in place Concave shape designed to prevent wrinkles Built from solid and sturdy wood Natural finish protects fabrics and looks nice 50 hangers per box
This item ships directly from the manufacturer and may be shipped separately from other items in your order.
Product Specifications/Installation Information
Manufacturer: Proman
Need large quantities? Click here for bulk ordering.


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American author, poet and activist Terry Tempest Williams will present two lectures at Clarion University: 7:30 p.m. April 24 in Rhoades Center at Venango College, Oil City, and 10:30 a.m. April 25 in 250/252 Gemmell Student Complex in Clarion. Both presentations are free and open to the public.
Known as a "citizen writer," Williams emphasizes the importance of the environment, women's health, freedom of speech, and other hot-button issues. As her bio states, "she has consistently shown us how environmental issues are social issues that ultimately become matters of justice."
Williams has received both critical acclaim and award recognition for her writing and activism. She has written 11 books, the most recent of which is "When Women Were Birds," published in 2012 and inspired by the journals of her late mother. Her work has appeared in The New Yorker, The New York Times, Orion Magazine and numerous anthologies worldwide.
Clarion University is the high-achieving, nationally recognized, comprehensive university that delivers a personal and challenging academic experience.


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Strike ballot over salary cuts
Members of The University and College Union will be balloted for strike action in a row over pay.
The action comes after Sunderland College announced plans to cut the salaries of more than 150 lecturers by £10,000 and downgrade 70% of its teaching workforce to inferior pay grades.
The union has accused the college of trying to deliver teaching on the cheap and using the current funding difficulties in further education as an excuse to cut staff pay.
The ballot will close on Friday 18 May.
– Iain Owens, UCU regional official
Nobody is blind to the funding challenges facing further education at the moment but there is no excuse for cutting pay in this way. The college's actions are completely disproportionate and seem little more than an attempt to deliver teaching on the cheap.
– Nigel Harrett, vice principal curriculum and student support
This is an extremely challenging time for Colleges across England as funding is cut, forcing savings to be made. We understand the union has a job to do on behalf of its members and we have a job to do on behalf of both our staff and our students – by securing the long term future and viability of the College.
We have an amount of money to save and are looking at various ways of making
those savings and have started from a 'worst case scenario


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SOURCE Cancer and Careers
Cancer and Careers' 4th Annual National Conference on Work & Cancer to Help Address Concerns
NEW YORK, June 10, 2014 /PRNewswire/ -- Half of unemployed cancer survivors looking for work worry that prospective employers would treat them differently if they knew about their cancer, according to new national survey results from Cancer and Careers, the only U.S. organization solely dedicated to serving the growing population of people working during and after cancer treatment.
The online survey, conducted by Harris Poll on behalf of Cancer and Careers, was designed to better understand the needs and attitudes of unemployed U.S. cancer survivors who are currently looking for work. The study interviewed 201 job-seeking patients and survivors (aged 18+) from November, 2013 through February, 2014. Results showed that while survivors overwhelmingly feel that work could actually aid in their recovery, more than half (61%) said they were at least somewhat concerned potential employers would find out about their cancer diagnosis and therefore not hire them.
"Cancer survivors, particularly those who took time off to focus on their treatment and recovery, may have a harder time re-entering the workplace with their unique circumstances," said Julie Jansen, career and executive coach, and Cancer and Careers consulting career coach. "However, with the right preparation and motivation, I believe cancer survivors can not only find the job or career they're looking for, but they can thrive in and out of the workplace."
While the survey found that financial necessity is the driving factor behind most cancer survivors' desire to return to work, about four in ten said they feel well enough to work (39%); more than a third want to maintain a sense of normalcy in their lives (36%); and roughly three in ten want to feel productive (31%) and desire a continuation of their career path (30%).
On June 13, Cancer and Careers will host the 4th Annual National Conference on Work & Cancer in New York City to address many of the challenges uncovered in the survey. The day-long conference explores the complexities people face-job search, health insurance, legal issues, working through treatment, job re-entry and more-as they try to balance their cancer treatment and recovery with employment.
According to the survey, job-seeking patients and survivors agreed that securing a job in a good work environment is essential to their ultimate wellbeing:
"For people going through or recovering from cancer treatment, the prospect of searching for a job can be daunting," said Kate Sweeney, executive director, Cancer and Careers. "The Cancer and Careers national conference is a great opportunity for survivors to learn how to help make the process easier, as well as learn about our free resources and services like resume review, career coaching, and educational events to help tackle work-related challenges."
The 4th Annual National Conference on Work & Cancer is free to attend. Registration is available at http://www.cancerandcareers.org/en/community/events/conference.
About the Survey
Cancer and Careers commissioned Harris Poll to conduct this survey to better understand the attitudes and behaviors of unemployed people with cancer. A total of 201 respondents participated in the research. Respondents were Americans 18 years of age or older, diagnosed with cancer and unemployed but looking for work. The interviews were conducted online, between November 11, 2013 and February 25, 2014. The data were weighted as needed for age, sex, race/ethnicity, education, region household income, as well as based on status of diagnosis and if respondents were able to find an organization or website that is dedicated to providing information on how to look for work after a cancer diagnosis.
About Cancer and Careers
Cancer and Careers empowers and educates people with cancer to thrive in their workplaces by providing expert advice, interactive tools and educational events. Cancer and Careers' websites in English and Spanish inform nearly 300,000 visitors per year. Cancer and Careers has trained more than 1,600 oncology health care professionals, and its services are used by 86 percent of the top cancer centers in the United States. For more information, please visit www.cancerandcareers.org.
About Nielsen & The Harris Poll
On February 3, 2014, Nielsen acquired Harris Interactive and The Harris Poll. Nielsen Holdings N.V. (NYSE: NLSN) is a global information and measurement company with leading market positions in marketing and consumer information, television and other media measurement, online intelligence and mobile measurement. Nielsen has a presence in approximately 100 countries, with headquarters in New York, USA and Diemen, the Netherlands. For more information, visit www.nielsen.com.
©2012 PR Newswire. All Rights Reserved.
Police said a forklift operator had just finished stacking the ceramic tiles on a wooden pallet on a top shelf when he noticed the pallet tipping.More >
Police said a forklift operator had just finished stacking the ceramic tiles on a wooden pallet on a top shelf when he noticed the pallet tipping.More >
Posts on several social media sites, including Twitter and Tumblr, claim to show nude photographs of the Academy Award-winning actress.More >
Posts on several social media sites, including Twitter and Tumblr, claim to show nude photographs of the Academy Award-winning actress.More >


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HOUSTON (Bloomberg) -- Oil rigs targeting oil in the U.S. declined by 25 this week to 1,564, according to Baker Hughes Inc. The drop was the largest since December 2012. Total rigs fell by 17 to 1,896, data posted on the company's website s ...
HAMILTON, Bermuda (Bloomberg) -- North Atlantic Drilling Ltd., the rig-owner controlled by billionaire John Fredriksen, will hand OAO Rosneft a stake valued at more than $1 billion in return for land rigs and cash, deepening ties amid sanct ...
LONDON (Bloomberg) -- BP Plc won't face a $256 billion lawsuit brought by a whistle-blower who claimed the company's Atlantis oil production platform in the Gulf of Mexico was unsafe. ...
A newly developed, 11¾-in., expandable liner hanger packer (ELHP) system made it possible to overcome the challenges of drilling Saudi Aramco's first deepwater well, a rank wildcat in the Red Sea.
Despite a variety of interfering factors, U.S. activity remains at a high level, aided by the industry's technical and efficiency gains. Canada continues to slowly rebound on the strength of oil activity, while Mexico remains at a lower level.
The South Texas fairway of the Eagle Ford/Pearsall shale has taken on the feel of a more than 400-mi-long trade mart this year, as new players shell out top dollar to gain a share of what are among the highest recovery rates in the unconventional sector, and a play with plenty of room to grow.
The deepwater, lightweight riser system, incorporating improvements derived from nearly a decade of operation, can extend the water depth range of rigs to 8,000 ft.
Exploration offshore Congo is moving into deeper water, with discoveries, such as Moho Bilondo, helping to de-risk the petroleum system.
As operators push Norwegian E&P activity close to record highs, the government and industry are working together to plan future upstream growth prudently while keeping costs under control.
In the same way that operators, service companies and manufacturers have switched gears to respond to the changing oil and gas landscape offshore Norway, the UK and mainland Europe, the organizers of this year's Offshore Northern Seas (ONS) event have also updated their focus.
This is the most comprehensive handbook in advanced drilling technology, guiding the petroleum engineer to mitigate risks, manage the reservoir effectively and recognize new opportunities.
This 2‐hour documentary is the most comprehensive video available about oil and gas drilling.
U.S. Natural Gas (Henry Hub): $3.854/Mcf
West Texas Intermediate: $93.76/bbl
Brent Blend: $102.48/bbl
U.S.: 8.335 MMbpd (June 2014)
World: 90.23 MMbpd (June 2014)
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