View Single Post
Old 2008-09-16, 23:19   #10
ATH
Einyen
 
ATH's Avatar
 
Dec 2003
Denmark

2·5·172 Posts
Default

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=2p-1*(2p-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
ATH is offline   Reply With Quote