Share N+/-1 Primality Proofs

[MDaniello]

Now that the worker queue was emptied, the FDB processed the N+/-1 proofs too (i guess they have a low priority).
This is what i had in queue:

(1538^356+1)/(1538^4+1)   N-1, 1122 digits
(7023^1153-1)/7022   N-1, 4432 digits
I(12652)^2+2   N-1, 5288 digits
(56^1698-1)^2-2 N+1, 5937 digits
(60^1717+1)^2-2   N+1, 6107 digits
(2^10367+1)^2-2   N+1, 6242 digits
(252^1330-1)^2-2   N+1, 6388 digits
(432^1227+1)^2-2   N+1, 6468 digits
(92^1795+1)^2-2  N+1, 7050 digits
(156^1663-1)^2-2   N+1, 7295 digits
(1507^2521+1)/1508   N-1, 8009 digits

I'm still working on other numbers i have previously spotted as candidates.

[MDaniello]

(9667^1201-1)/9666   N-1   4783 digits
(154^1495-1)^2-2   N+1   6541 digits
(2^21701-1)*138769890-1   N+1   6541 digits
(2^21701-1)*138769890+1   N-1   6541 digits
(86^2053-1)^2-2   N+1   7944 digits
(58^2354+1)^2-2   N+1   8303 digits
(10^4299-1)^2-2   N+1   8598 digits
117371^2015*2+1   N-1   10216 digits

[MDaniello]

(21351113^128+1)/2   N-1   938 digits
(2^132049-1)*185056+1   N-1   39756 digits
(2^132049-1)*30690+1   N-1   39756 digits

[MDaniello]

10*I(23856)-1  N+/-1  4987 digits
70^633-71   N+1 1168 digits
91^593-92   N+1   1162 digits
410^413-411   N+1  1080 digits
44174...01   N-1   1033 digits
126^465-127   N+1   977 digits
69^351+70   N-1   646 digits

[MDaniello]

2^18942-63      N-1   5703 digits
2*I(23918)+1      N+/-1   4999 digits
(5093^991-1)/5092   N-1   3670 digits
8933594132...01   N-1   532 digits
8453207264...41   N-1   329 digits

[MDaniello]

(2^86243-1)*702850+1   N-1   25968 digits
(2^86243-1)*1311784+1  N+/-1   25968 digits
(2^86243-1)*58818+1   N-1   25967 digits
(2^86243-1)*42844+1   N-1   25967 digits
(22^8643-1)^2-2   N+1   23206 digits
2825659559...01   N-1   469 digits

[chris2be8]

Hello,

There are now over 121000 PRPs under 3000 digits in factordb. I'm running a script to prove simple cases prime by N-1 if N-1 has algebraic factors (it handles (b^p-1)/(b-1) and (b^p+1)/(b+1) for various b and p). I've got to 444 digits but it's likely to take a few says to reach 3000 digits. And it'll only prove a few % of the PRPs.

This lot are probably related to all the small junk that's appearing in factordb.

Chris

[chris2be8]

And the script has finished:

Stopping at 3010 digits number 4 (5347 proved prime (tried to factor 12735 N-1's, 1 new factor added, 427 fully factored))

Although there were very few matching numbers above 2175 digits.

Most of the 12735 times it tried to factor N-1 it found several factors factordb already knew of, but probably didn't know divided N-1. But I don't know how many because the script didn't fetch N-1 to see how many factors it had before trying to factor it.

I'll run it again in a few days. There are probably quite a few where N-1 has factors under 90 digits and a proof will be possible once they are factored. Also I've enhanced it to check for a few more cases, eg GFNs (b^2^n+1).

Chris

[chris2be8]

Second run finished:

Stopping at 3011 digits number 3 (2874 proved prime (tried to factor 11564 N-1's, 0 new factors added, 187 fully factored))

Most of the successes were of the form (b^n+1)/(b^2+1) since I've enhanced the script to search for that. I don't intend to run it again unless I find another reasonably common case I can program it to handle. But that should have saved quite a bit of time generating certificates.

Chris

[chris2be8]

I've noticed an interesting set of PRPs in factordb (all 1000 digits):

1100000001977145547 	10^999+12142617231 
1100000001977145688 	(10^999+12142617231)*2-1
1100000001977145775 	((10^999+12142617231)*2-1)*2-1

Proving the first one will enable N+1 proofs the other two are prime.

Chris