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Einyen
Dec 2003
Denmark
3·52·41 Posts
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Updated list:
Code:
p: factor(s) of 2p-1*(2p-1) + 1
------------------------------------------------------------------
2: prime
3: prime
5: 7 , 71
7: 11 , 739
13: prime
17: 7 , 11 , 111556741
19: prime
31: 29 , 71 , 137 , 1621 , 5042777503
61: 2432582681 , 1092853292237112554142488617
89: 7
107: 7 , 11 , 67
127: 11 , 107 , 261697
521: 7 , 71
607: 11
1279: 72353441721527140856665601867
2203: 60449 , 1498429 , 711309659, 1418050069
2281: 197 , 557 , 1999 , 92033
3217: 11
4253: 7 , 53 , 8731 , 2353129 , 50820071
4423: 2163571
9689: 7 , 211 , 49922567
9941: 7 , 67 , 1605697 , 194147011
11213: 7
19937: 7 , 11 , 1129 , 168457
21701: 7
23209: 35603 , 620377
44497: 11 , 13259 , 16177141 , 896297147
86243: 7 , 29 , 301123 , 26072029
110503: 491 , 1493 , 1529761
132049: 194528547122653
216091: 4673 , 6920341
756839: 7
859433: 7
1257787: 11
1398269: 7 , 53 , 12713 , 17425081 , 199979189
2976221: 7 , 71
3021377: 7 , 11 , 49603
6972593: 7 , 6007 , 8392897 , 52193821
13466917: 11 , 45007
20996011: 1552147 , 114242767
24036583: 149
25964951: 7
30402457: 11
32582657: 7 , 11 , 67 , 34549 , 127541
37156667: 7 , 11 , 44753 , 202577 , 1282451377
42643801: 3593 , 7089208037
43112609: 7 , 211 , 70121 , 71647 , 1846524311
57885161: 7 , 22127627
74207281: No factor < 6*1012
77232917: 7 , 11 , 11587
82589933: 7 , 67 , 599 , 7347113 , 14416229
So of the now 51 known perfect numbers P=2 p-1*(2 p-1), P+1 is only still prime for p=2,3,13 and 19, and status unknown for p=74207281.
Last fiddled with by ATH on 2020-01-30 at 03:13
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