<Table> <Tr> <Th> Rank </Th> <Th> p </Th> <Th> Perfect number </Th> <Th> Digits </Th> <Th> Year </Th> <Th> Discoverer </Th> </Tr> <Tr> <Td> </Td> <Td> </Td> <Td> 6 </Td> <Td> </Td> <Td> 4th century B.C. </Td> <Td> Euclid </Td> </Tr> <Tr> <Td> </Td> <Td> </Td> <Td> 28 </Td> <Td> </Td> <Td> 4th century B.C. </Td> <Td> Euclid </Td> </Tr> <Tr> <Td> </Td> <Td> 5 </Td> <Td> 496 </Td> <Td> </Td> <Td> 4th century B.C. </Td> <Td> Euclid </Td> </Tr> <Tr> <Td> </Td> <Td> 7 </Td> <Td> 8128 </Td> <Td> </Td> <Td> 4th century B.C. </Td> <Td> Euclid </Td> </Tr> <Tr> <Td> 5 </Td> <Td> 13 </Td> <Td> 33550336 </Td> <Td> 8 </Td> <Td> 1456 </Td> <Td> First seen in a medieval manuscript , Munich , Bayerische Staatsbibliothek , CLM 14908 , fol. 33 </Td> </Tr> <Tr> <Td> 6 </Td> <Td> 17 </Td> <Td> 8589869056 </Td> <Td> 10 </Td> <Td> 1588 </Td> <Td> Cataldi </Td> </Tr> <Tr> <Td> 7 </Td> <Td> 19 </Td> <Td> 137438691328 </Td> <Td> 12 </Td> <Td> 1588 </Td> <Td> Cataldi </Td> </Tr> <Tr> <Td> 8 </Td> <Td> 31 </Td> <Td> 2305843008139952128 </Td> <Td> 19 </Td> <Td> 1772 </Td> <Td> Euler </Td> </Tr> <Tr> <Td> 9 </Td> <Td> 61 </Td> <Td> 265845599156 ... 615953842176 </Td> <Td> 37 </Td> <Td> 1883 </Td> <Td> Pervushin </Td> </Tr> <Tr> <Td> 10 </Td> <Td> 89 </Td> <Td> 191561942608 ... 321548169216 </Td> <Td> 54 </Td> <Td> 1911 </Td> <Td> Powers </Td> </Tr> <Tr> <Td> 11 </Td> <Td> 107 </Td> <Td> 131640364585 ... 117783728128 </Td> <Td> 65 </Td> <Td> 1914 </Td> <Td> Powers </Td> </Tr> <Tr> <Td> 12 </Td> <Td> 127 </Td> <Td> 144740111546 ... 131199152128 </Td> <Td> 77 </Td> <Td> 1876 </Td> <Td> Lucas </Td> </Tr> <Tr> <Td> 13 </Td> <Td> 521 </Td> <Td> 235627234572 ... 160555646976 </Td> <Td> 314 </Td> <Td> 1952 </Td> <Td> Robinson </Td> </Tr> <Tr> <Td> 14 </Td> <Td> 607 </Td> <Td> 141053783706 ... 759537328128 </Td> <Td> 366 </Td> <Td> 1952 </Td> <Td> Robinson </Td> </Tr> <Tr> <Td> 15 </Td> <Td> 1,279 </Td> <Td> 541625262843 ... 764984291328 </Td> <Td> 770 </Td> <Td> 1952 </Td> <Td> Robinson </Td> </Tr> <Tr> <Td> 16 </Td> <Td> 2,203 </Td> <Td> 108925835505 ... 834453782528 </Td> <Td> 1,327 </Td> <Td> 1952 </Td> <Td> Robinson </Td> </Tr> <Tr> <Td> 17 </Td> <Td> 2,281 </Td> <Td> 994970543370 ... 675139915776 </Td> <Td> 1,373 </Td> <Td> 1952 </Td> <Td> Robinson </Td> </Tr> <Tr> <Td> 18 </Td> <Td> 3,217 </Td> <Td> 335708321319 ... 332628525056 </Td> <Td> 1,937 </Td> <Td> 1957 </Td> <Td> Riesel </Td> </Tr> <Tr> <Td> 19 </Td> <Td> 4,253 </Td> <Td> 182017490401 ... 437133377536 </Td> <Td> 2,561 </Td> <Td> 1961 </Td> <Td> Hurwitz </Td> </Tr> <Tr> <Td> 20 </Td> <Td> 4,423 </Td> <Td> 407672717110 ... 642912534528 </Td> <Td> 2,663 </Td> <Td> 1961 </Td> <Td> Hurwitz </Td> </Tr> <Tr> <Td> 21 </Td> <Td> 9,689 </Td> <Td> 114347317530 ... 558429577216 </Td> <Td> 5,834 </Td> <Td> 1963 </Td> <Td> Gillies </Td> </Tr> <Tr> <Td> 22 </Td> <Td> 9,941 </Td> <Td> 598885496387 ... 324073496576 </Td> <Td> 5,985 </Td> <Td> 1963 </Td> <Td> Gillies </Td> </Tr> <Tr> <Td> 23 </Td> <Td> 11,213 </Td> <Td> 395961321281 ... 702691086336 </Td> <Td> 6,751 </Td> <Td> 1963 </Td> <Td> Gillies </Td> </Tr> <Tr> <Td> 24 </Td> <Td> 19,937 </Td> <Td> 931144559095 ... 790271942656 </Td> <Td> 12,003 </Td> <Td> 1971 </Td> <Td> Tuckerman </Td> </Tr> <Tr> <Td> 25 </Td> <Td> 21,701 </Td> <Td> 100656497054 ... 255141605376 </Td> <Td> 13,066 </Td> <Td> 1978 </Td> <Td> Noll & Nickel </Td> </Tr> <Tr> <Td> 26 </Td> <Td> 23,209 </Td> <Td> 811537765823 ... 603941666816 </Td> <Td> 13,973 </Td> <Td> 1979 </Td> <Td> Noll </Td> </Tr> <Tr> <Td> 27 </Td> <Td> 44,497 </Td> <Td> 365093519915 ... 353031827456 </Td> <Td> 26,790 </Td> <Td> 1979 </Td> <Td> Nelson & Slowinski </Td> </Tr> <Tr> <Td> 28 </Td> <Td> 86,243 </Td> <Td> 144145836177 ... 957360406528 </Td> <Td> 51,924 </Td> <Td> 1982 </Td> <Td> Slowinski </Td> </Tr> <Tr> <Td> 29 </Td> <Td> 110,503 </Td> <Td> 136204582133 ... 233603862528 </Td> <Td> 66,530 </Td> <Td> </Td> <Td> Colquitt & Welsh </Td> </Tr> <Tr> <Td> 30 </Td> <Td> 132,049 </Td> <Td> 131451295454 ... 491774550016 </Td> <Td> 79,502 </Td> <Td> </Td> <Td> Slowinski </Td> </Tr> <Tr> <Td> 31 </Td> <Td> 216,091 </Td> <Td> 278327459220 ... 416840880128 </Td> <Td> 130,100 </Td> <Td> 1985 </Td> <Td> Slowinski </Td> </Tr> <Tr> <Td> 32 </Td> <Td> 756,839 </Td> <Td> 151616570220 ... 600565731328 </Td> <Td> 455,663 </Td> <Td> </Td> <Td> Slowinski & Gage </Td> </Tr> <Tr> <Td> 33 </Td> <Td> 859,433 </Td> <Td> 838488226750 ... 540416167936 </Td> <Td> 517,430 </Td> <Td> </Td> <Td> Slowinski & Gage </Td> </Tr> <Tr> <Td> 34 </Td> <Td> 1,257,787 </Td> <Td> 849732889343 ... 028118704128 </Td> <Td> 757,263 </Td> <Td> </Td> <Td> Slowinski & Gage </Td> </Tr> <Tr> <Td> 35 </Td> <Td> 1,398,269 </Td> <Td> 331882354881 ... 017723375616 </Td> <Td> 841,842 </Td> <Td> </Td> <Td> Armengaud , Woltman , et al .
<Table> <Tr> <Th> Rank </Th> <Th> p </Th> <Th> Perfect number </Th> <Th> Digits </Th> <Th> Year </Th> <Th> Discoverer </Th> </Tr> <Tr> <Td> </Td> <Td> </Td> <Td> 6 </Td> <Td> </Td> <Td> 4th century B.C. </Td> <Td> Euclid </Td> </Tr> <Tr> <Td> </Td> <Td> </Td> <Td> 28 </Td> <Td> </Td> <Td> 4th century B.C. </Td> <Td> Euclid </Td> </Tr> <Tr> <Td> </Td> <Td> 5 </Td> <Td> 496 </Td> <Td> </Td> <Td> 4th century B.C. </Td> <Td> Euclid </Td> </Tr> <Tr> <Td> </Td> <Td> 7 </Td> <Td> 8128 </Td> <Td> </Td> <Td> 4th century B.C. </Td> <Td> Euclid </Td> </Tr> <Tr> <Td> 5 </Td> <Td> 13 </Td> <Td> 33550336 </Td> <Td> 8 </Td> <Td> 1456 </Td> <Td> First seen in a medieval manuscript , Munich , Bayerische Staatsbibliothek , CLM 14908 , fol. 33 </Td> </Tr> <Tr> <Td> 6 </Td> <Td> 17 </Td> <Td> 8589869056 </Td> <Td> 10 </Td> <Td> 1588 </Td> <Td> Cataldi </Td> </Tr> <Tr> <Td> 7 </Td> <Td> 19 </Td> <Td> 137438691328 </Td> <Td> 12 </Td> <Td> 1588 </Td> <Td> Cataldi </Td> </Tr> <Tr> <Td> 8 </Td> <Td> 31 </Td> <Td> 2305843008139952128 </Td> <Td> 19 </Td> <Td> 1772 </Td> <Td> Euler </Td> </Tr> <Tr> <Td> 9 </Td> <Td> 61 </Td> <Td> 265845599156 ... 615953842176 </Td> <Td> 37 </Td> <Td> 1883 </Td> <Td> Pervushin </Td> </Tr> <Tr> <Td> 10 </Td> <Td> 89 </Td> <Td> 191561942608 ... 321548169216 </Td> <Td> 54 </Td> <Td> 1911 </Td> <Td> Powers </Td> </Tr> <Tr> <Td> 11 </Td> <Td> 107 </Td> <Td> 131640364585 ... 117783728128 </Td> <Td> 65 </Td> <Td> 1914 </Td> <Td> Powers </Td> </Tr> <Tr> <Td> 12 </Td> <Td> 127 </Td> <Td> 144740111546 ... 131199152128 </Td> <Td> 77 </Td> <Td> 1876 </Td> <Td> Lucas </Td> </Tr> <Tr> <Td> 13 </Td> <Td> 521 </Td> <Td> 235627234572 ... 160555646976 </Td> <Td> 314 </Td> <Td> 1952 </Td> <Td> Robinson </Td> </Tr> <Tr> <Td> 14 </Td> <Td> 607 </Td> <Td> 141053783706 ... 759537328128 </Td> <Td> 366 </Td> <Td> 1952 </Td> <Td> Robinson </Td> </Tr> <Tr> <Td> 15 </Td> <Td> 1,279 </Td> <Td> 541625262843 ... 764984291328 </Td> <Td> 770 </Td> <Td> 1952 </Td> <Td> Robinson </Td> </Tr> <Tr> <Td> 16 </Td> <Td> 2,203 </Td> <Td> 108925835505 ... 834453782528 </Td> <Td> 1,327 </Td> <Td> 1952 </Td> <Td> Robinson </Td> </Tr> <Tr> <Td> 17 </Td> <Td> 2,281 </Td> <Td> 994970543370 ... 675139915776 </Td> <Td> 1,373 </Td> <Td> 1952 </Td> <Td> Robinson </Td> </Tr> <Tr> <Td> 18 </Td> <Td> 3,217 </Td> <Td> 335708321319 ... 332628525056 </Td> <Td> 1,937 </Td> <Td> 1957 </Td> <Td> Riesel </Td> </Tr> <Tr> <Td> 19 </Td> <Td> 4,253 </Td> <Td> 182017490401 ... 437133377536 </Td> <Td> 2,561 </Td> <Td> 1961 </Td> <Td> Hurwitz </Td> </Tr> <Tr> <Td> 20 </Td> <Td> 4,423 </Td> <Td> 407672717110 ... 642912534528 </Td> <Td> 2,663 </Td> <Td> 1961 </Td> <Td> Hurwitz </Td> </Tr> <Tr> <Td> 21 </Td> <Td> 9,689 </Td> <Td> 114347317530 ... 558429577216 </Td> <Td> 5,834 </Td> <Td> 1963 </Td> <Td> Gillies </Td> </Tr> <Tr> <Td> 22 </Td> <Td> 9,941 </Td> <Td> 598885496387 ... 324073496576 </Td> <Td> 5,985 </Td> <Td> 1963 </Td> <Td> Gillies </Td> </Tr> <Tr> <Td> 23 </Td> <Td> 11,213 </Td> <Td> 395961321281 ... 702691086336 </Td> <Td> 6,751 </Td> <Td> 1963 </Td> <Td> Gillies </Td> </Tr> <Tr> <Td> 24 </Td> <Td> 19,937 </Td> <Td> 931144559095 ... 790271942656 </Td> <Td> 12,003 </Td> <Td> 1971 </Td> <Td> Tuckerman </Td> </Tr> <Tr> <Td> 25 </Td> <Td> 21,701 </Td> <Td> 100656497054 ... 255141605376 </Td> <Td> 13,066 </Td> <Td> 1978 </Td> <Td> Noll & Nickel </Td> </Tr> <Tr> <Td> 26 </Td> <Td> 23,209 </Td> <Td> 811537765823 ... 603941666816 </Td> <Td> 13,973 </Td> <Td> 1979 </Td> <Td> Noll </Td> </Tr> <Tr> <Td> 27 </Td> <Td> 44,497 </Td> <Td> 365093519915 ... 353031827456 </Td> <Td> 26,790 </Td> <Td> 1979 </Td> <Td> Nelson & Slowinski </Td> </Tr> <Tr> <Td> 28 </Td> <Td> 86,243 </Td> <Td> 144145836177 ... 957360406528 </Td> <Td> 51,924 </Td> <Td> 1982 </Td> <Td> Slowinski </Td> </Tr> <Tr> <Td> 29 </Td> <Td> 110,503 </Td> <Td> 136204582133 ... 233603862528 </Td> <Td> 66,530 </Td> <Td> </Td> <Td> Colquitt & Welsh </Td> </Tr> <Tr> <Td> 30 </Td> <Td> 132,049 </Td> <Td> 131451295454 ... 491774550016 </Td> <Td> 79,502 </Td> <Td> </Td> <Td> Slowinski </Td> </Tr> <Tr> <Td> 31 </Td> <Td> 216,091 </Td> <Td> 278327459220 ... 416840880128 </Td> <Td> 130,100 </Td> <Td> 1985 </Td> <Td> Slowinski </Td> </Tr> <Tr> <Td> 32 </Td> <Td> 756,839 </Td> <Td> 151616570220 ... 600565731328 </Td> <Td> 455,663 </Td> <Td> </Td> <Td> Slowinski & Gage </Td> </Tr> <Tr> <Td> 33 </Td> <Td> 859,433 </Td> <Td> 838488226750 ... 540416167936 </Td> <Td> 517,430 </Td> <Td> </Td> <Td> Slowinski & Gage </Td> </Tr> <Tr> <Td> 34 </Td> <Td> 1,257,787 </Td> <Td> 849732889343 ... 028118704128 </Td> <Td> 757,263 </Td> <Td> </Td> <Td> Slowinski & Gage </Td> </Tr> <Tr> <Td> 35 </Td> <Td> 1,398,269 </Td> <Td> 331882354881 ... 017723375616 </Td> <Td> 841,842 </Td> <Td> </Td> <Td> Armengaud , Woltman , et al .
list of perfect numbers from 1 to 100
list of perfect numbers from 1 to 100
6 28
6 28