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Old 2008-05-29, 08:25   #7
henryzz
Just call me Henry
 
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"David"
Sep 2007
Cambridge (GMT/BST)

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Quote:
Originally Posted by ATH View Post
I trialfactored P+1 for the 44 known perfect numbers P and did ECM on 1 of them:

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
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: ?
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

So perfectnumber+1 are prime for p=2,3,13 and 19 and unknown for p=132049 (79502 digits) which I trialfactored to 18*109.
gmp-ecm doesnt think p=132049 is prp
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