20160123, 16:09  #12  
"Jeppe"
Jan 2016
Denmark
10100110_{2} Posts 
Quote:
42643801: 3593, 7089208037 43112609: 7, 211, 70121, 71647, 1846524311 (was in 2008 post by ATH) 57885161: 7, 22127627 74207281: ? My trial factoring with the latest perfect number, incremented by one, has not yielded any divisors under $75\cdot 10^9$. /JeppeSN 

20160123, 17:00  #13 
Einyen
Dec 2003
Denmark
101111010111_{2} Posts 
Yeah for 57885161 there is also a factor: 22127627.
For p=74207281, I trial factored 2^{p1}*(2^{p}1) + 1 up to 4.46*10^{12} with no factor. 
20160126, 12:43  #14 
"Jeppe"
Jan 2016
Denmark
A6_{16} Posts 
Do you know if anyone is going further with trial factoring this beast, $2^{74207280}(2^{74207281}1)+1$, or even do a primality test of it? It may turn out to be very hard to find a prime factor for this one? /JeppeSN

20160126, 17:20  #15 
Einyen
Dec 2003
Denmark
7·433 Posts 
Yeah the chance of finding a factor is very low, and doing a primality test is impossible. At 44.7 million digits only an LL test would be fast enough but it will not work on a number of this form. There is no software I can think of that can even do a PRP test.
Anyway these numbers are not really that important I think, it was just a question a user asked almost 8 years ago which turned into this tiny trial factoring effort. I have never seen any interest in "perfect numbers + 1" anywhere else. 
20160127, 06:38  #17 
Einyen
Dec 2003
Denmark
7×433 Posts 
Yes true, but that was for 79502 digits. I do not think programs like PFGW, which can do the N1 test, can handle 44 million digits or anywhere near this size.
A 44 million digit LL test would take 1014 days on the very fastest computers / graphic cards with Prime95 / CudaLucas, and an N1 test would take longer than that. I do not think PFGW can save the test during it and restart, but I'm not certain about that. 
20160127, 08:43  #18  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10010001101110_{2} Posts 
Quote:
Quote:


20160127, 12:36  #19  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
2×2,909 Posts 
Quote:
Possible if someone wants to spend several months on it I think. Last fiddled with by henryzz on 20160127 at 12:46 

20160127, 14:04  #20 
"Jeppe"
Jan 2016
Denmark
2×83 Posts 
On my Windows system, it crashes.
I try with: Code:
.\pfgw64.exe q"2^74207280*(2^742072811)+1" t f0 h"jeppe_M74207281.txt" pfgw32.exe with the same parameters crashes as well, on my machine here. Using the binaries from .7z file here: http://sourceforge.net/projects/openpfgw/ Can anyone else get to a point where the N1 test actually progresses? /JeppeSN 
20160127, 15:40  #21 
Sep 2002
Database er0rr
111000000110_{2} Posts 
It is much quicker to run a default 3PRP test, rather than a fully blown N1 test. If that goes fine, I am sure the authors will fix up PFGW for you
Here, I would run on linux: ./pfgw64 q"2^74207280*(2^742072811)+1" f0 The chance it will be prime is next to zero, but you will know! 
20160127, 16:52  #22 
"Jeppe"
Jan 2016
Denmark
166_{10} Posts 
Maybe it is smarter to sieve even further before attempting a PRP or primality test. After all, what we want to add to ATH's table above is the smallest prime factor, and it is too optimistic to hope the primality test will result in N being its own smallest prime factor. /JeppeSN

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