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 2020-03-19, 11:19 #419 MDaniello     May 2019 Rome, Italy 2×17 Posts Quarantine is boring 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: Code: (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.
 2020-03-24, 20:34 #420 MDaniello     May 2019 Rome, Italy 2×17 Posts Code: (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
 2020-04-16, 07:54 #421 MDaniello     May 2019 Rome, Italy 2×17 Posts Code: (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
 2020-05-28, 22:36 #422 MDaniello     May 2019 Rome, Italy 2×17 Posts Code: 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
 2020-09-28, 09:56 #423 MDaniello     May 2019 Rome, Italy 428 Posts Code: 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
 2020-10-19, 08:38 #424 MDaniello     May 2019 Rome, Italy 428 Posts Code: (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
 2020-11-20, 16:56 #425 chris2be8     Sep 2009 197510 Posts 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
 2020-11-22, 16:43 #426 chris2be8     Sep 2009 36678 Posts And the script has finished: Code: 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
 2020-11-25, 16:49 #427 chris2be8     Sep 2009 111101101112 Posts Second run finished: Code: 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
 2020-11-29, 16:52 #428 chris2be8     Sep 2009 52·79 Posts I've noticed an interesting set of PRPs in factordb (all 1000 digits): Code: 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 Last fiddled with by chris2be8 on 2020-11-29 at 16:55 Reason: Typo

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