# Finding prime numbers which are generated by other primes

How do you...

1. Find the prime(s) generated by the alternate primes 2,5,11,17.

2. Find the prime(s) generated by the first five primes 2,3,5,7,11.

We are allowed to use all arithmetic operators.

• What do you mean? – lulu Apr 3 '18 at 13:52
• The only times I have read about "generating primes" the context has been an explicit algorithm. Thus, for instance, Euclid's method let's us find a new prime if given a finite list of primes $\{p_1,\cdots, p_k\}$ by factoring $\prod p_i+1$. But here no algorithm is specified. – lulu Apr 3 '18 at 13:55
• Apologies, it would be in reference to Euclid's method... – MathsUndergrad Apr 3 '18 at 13:56
• Please edit your post to reflect that. Also...where is the difficulty? Just multiply the given primes and factor. It's a little tedious, perhaps, if you are doing it by hand but it is still trivial. – lulu Apr 3 '18 at 13:57
• I think this is a good question, however like lulu mentioned in comments, you need to add more info. – usiro Apr 4 '18 at 21:15

1. Your task is to find the prime factors of $2\cdot 5\cdot 11\cdot 17+1$, that are not among $2,5,11,17$.
2. Your task is to find the prime factors of $2\cdot 3\cdot 5\cdot 7\cdot 11+1$, that are not among $2,3,5,7,11$.
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