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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] [URL="http://factordb.com/index.php?id=1100000001439594752"](1538^356+1)/(1538^4+1)[/URL] N-1, 1122 digits [URL="http://factordb.com/index.php?id=1100000000492536998"](7023^1153-1)/7022[/URL] N-1, 4432 digits [URL="http://factordb.com/index.php?id=1100000000838749974"]I(12652)^2+2[/URL] N-1, 5288 digits [URL="http://factordb.com/index.php?id=1100000001085704672"](56^1698-1)^2-2[/URL] N+1, 5937 digits [URL="http://factordb.com/index.php?id=1100000000840392735"](60^1717+1)^2-2[/URL] N+1, 6107 digits [URL="http://factordb.com/index.php?id=1100000001156085695"](2^10367+1)^2-2[/URL] N+1, 6242 digits [URL="http://factordb.com/index.php?id=1100000001086615218"](252^1330-1)^2-2[/URL] N+1, 6388 digits [URL="http://factordb.com/index.php?id=1100000001114492513"](432^1227+1)^2-2[/URL] N+1, 6468 digits [URL="http://factordb.com/index.php?id=1100000001086297704"](92^1795+1)^2-2[/URL] N+1, 7050 digits [URL="http://factordb.com/index.php?id=1100000001086301950"](156^1663-1)^2-2[/URL] N+1, 7295 digits [URL="http://www.factordb.com/index.php?id=1100000001178102954"](1507^2521+1)/1508[/URL] N-1, 8009 digits [/CODE] I'm still working on other numbers i have previously spotted as candidates. |
[CODE]
[URL="http://factordb.com/index.php?id=1100000000493022786"](9667^1201-1)/9666[/URL] N-1 4783 digits [URL="http://factordb.com/index.php?id=1100000001086336158"](154^1495-1)^2-2[/URL] N+1 6541 digits [URL="http://factordb.com/index.php?id=1100000001419712630"](2^21701-1)*138769890-1[/URL] N+1 6541 digits [URL="http://factordb.com/index.php?id=1100000001419712577"](2^21701-1)*138769890+1[/URL] N-1 6541 digits [URL="http://factordb.com/index.php?id=1100000001086296878"](86^2053-1)^2-2[/URL] N+1 7944 digits [URL="http://factordb.com/index.php?id=1100000001085717141"](58^2354+1)^2-2[/URL] N+1 8303 digits [URL="http://factordb.com/index.php?id=1100000000799893138"](10^4299-1)^2-2[/URL] N+1 8598 digits [URL="http://factordb.com/index.php?id=1100000001136709909"]117371^2015*2+1[/URL] N-1 10216 digits [/CODE] |
[CODE]
[URL="http://factordb.com/index.php?id=1100000001459591120"](21351113^128+1)/2[/URL] N-1 938 digits [URL="http://www.factordb.com/index.php?id=1100000000271528297"](2^132049-1)*185056+1[/URL] N-1 39756 digits [URL="http://www.factordb.com/index.php?id=1100000000934910771"](2^132049-1)*30690+1[/URL] N-1 39756 digits [/CODE] |
[CODE]
[URL="http://www.factordb.com/index.php?id=1100000001351638991"]10*I(23856)-1[/URL] N+/-1 4987 digits [URL="http://factordb.com/index.php?id=1100000001499539614"]70^633-71[/URL] N+1 1168 digits [URL="http://www.factordb.com/index.php?id=1100000001489144849"]91^593-92[/URL] N+1 1162 digits [URL="http://www.factordb.com/index.php?id=1100000001489125751"]410^413-411[/URL] N+1 1080 digits [URL="http://www.factordb.com/index.php?id=1100000001485589035"]44174...01[/URL] N-1 1033 digits [URL="http://factordb.com/index.php?id=1100000001499541727"]126^465-127[/URL] N+1 977 digits [URL="http://www.factordb.com/index.php?id=1100000001499539725"]69^351+70[/URL] N-1 646 digits [/CODE] |
[CODE]
[URL="http://factordb.com/index.php?id=1100000000294461298"]2^18942-63[/URL] N-1 5703 digits [URL="http://factordb.com/index.php?id=1100000001392299969"]2*I(23918)+1[/URL] N+/-1 4999 digits [URL="http://www.factordb.com/index.php?id=1100000001523384215"](5093^991-1)/5092[/URL] N-1 3670 digits [URL="http://factordb.com/index.php?id=1100000001522182661"]8933594132...01[/URL] N-1 532 digits [URL="http://factordb.com/index.php?id=1100000001530760695"]8453207264...41[/URL] N-1 329 digits [/CODE] |
[CODE]
[URL="http://www.factordb.com/index.php?id=1100000001388804470"](2^86243-1)*702850+1[/URL] N-1 25968 digits [URL="http://www.factordb.com/index.php?id=1100000000273952855"](2^86243-1)*1311784+1[/URL] N+/-1 25968 digits [URL="http://www.factordb.com/index.php?id=1100000000934910828"](2^86243-1)*58818+1[/URL] N-1 25967 digits [URL="http://www.factordb.com/index.php?id=1100000000934910843"](2^86243-1)*42844+1[/URL] N-1 25967 digits [URL="http://www.factordb.com/index.php?id=1100000001087068428"](22^8643-1)^2-2[/URL] N+1 23206 digits [URL="http://factordb.com/index.php?id=1100000001578932112"]2825659559...01[/URL] N-1 469 digits [/CODE] |
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 |
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)) [/code] 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 |
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)) [/code] 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 |
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 [/code] Proving the first one will enable N+1 proofs the other two are prime. Chris |
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