Share N+/-1 Primality Proofs - Page 7

henryzz · 2012-02-28, 21:18

Add $ to the end of
^$([0-9]+)\^([0-9]+)\*([0-9]+)([+-])([0-9]+)$/([0-9]+)
to make
^$([0-9]+)\^([0-9]+)\*([0-9]+)([+-])([0-9]+)$/([0-9]+)$

Otherwise it lets lines like
(13^1479*19-1)/453707218/3^9
(2^5438*45-1)/16775191/3461^2
through which confuse the program.

henryzz · 2012-02-28, 21:57

The results from running on the first 1000 prps
(10^1631*14-41)/99 -
(19^1274*11-1)/10 -
(19^1287*3+1)/2 +
(2^5463*77-1)/615 -
(2^5502*69-1)/275 -

(2^5502*69-1)/275 N-1 needed help with factors from 2^5500-1
This was the only one that benefitted as all the others had already been found but still don't have a large enough factored part.

henryzz · 2012-02-28, 22:18

Results upto 2000 digits:

Code:

(10^1631*14-41)/99 -
(10^1676*34-43)/3357 -
(10^1719*2+9)/7 -
(10^1728*52-43)/9 -
(10^1729*49-31)/459 -
(10^1730*23-11)/2289 -
(10^1770*62-71)/9 +
(10^1781*31-301)/9 -
(10^1786*43-421)/9 -
(10^1788*44-17)/27 -
(10^1791*5-17)/33 -
(10^1794*88-61)/27 -
(10^1801*52-529)/9 +
(10^1865*25-7)/2493 -
(10^1891*4-13)/27 -
(10^1902*7-691)/9 -
(10^1908*14-41)/27 +
(10^1937*22-1)/219 -
(10^1937*8-77)/3 -
(10^1944*26-23)/3 -
(10^1951*5-53)/3 +
(10^1978*35-341)/9 -
(11^1612*8-1)/967 -
(11^1662*3-1)/2 -
(17^1455*5-1)/24564 -
(17^1458*10-1)/9 -
(17^1472*19-1)/18 -
(17^1555*4+1)/3 +
(19^1274*11-1)/10 -
(19^1287*3+1)/2 +
(19^1409*10-1)/9 -
(2^5463*77-1)/615 -
(2^5521*129-1)/257 -
(2^5701*21+1)/83 +
(2^5948*173-1)/44287 -
(2^5991*61-1)/124927 -
(2^6062*45-1)/89 -
(2^6066*193-1)/771 -
(2^6139*11-1)/21 -
(2^6140*17-1)/67 -
(2^6295*91-1)/727 -
(2^6394*85-1)/1359 -
(2^6481*105-1)/209 -
(2^6553*59-1)/117 -
(2^6557*113-1)/3615 -
(663^663*3+1)/2 +

I haven't checked these. Done enough for this evening.
If someone can provide a bigger list of prps I can check them easily. Soon I will add more forms to my program.

firejuggler · 2012-02-28, 23:33

(10^1728*52-43)/9 done

wblipp · 2012-02-29, 03:20

Great work! Sure beats my manual scans.

(2^6481*105-1)/209 - finished.

firejuggler · 2012-02-29, 04:23

done a few more

Batalov · 2012-02-29, 05:18

Everything base 10 is done long ago at M.Kamada's site. It only needs to be imported.

YuL · 2012-02-29, 08:58

Nice work henryzz. Done N-1 proof for (2^6140*17-1)/67.

henryzz · 2012-02-29, 13:07

Worth checking these prps found while trying to prove prps:

Code:

(((12^60+1)^2-2)*(11^1531-1)+1)/30943899 
(((12^60+1)^2-2)*(11^1661-1)+1)/2847 
(((12^60+1)^2-2)*(11^1737-1)+1)/3247287 
(((12^60+1)^2-2)*(7^1904+1)+1)/88320845 
(((12^60+1)^2-2)*(7^2056+1)+1)/55 
(((419#-8675309)*10^282+1)*10^1174-1)/535549 
((107^983+1)/108+1)/382908 
((10^1632*394-7)/9-1)/5031247566694608 
((10^1667*4-3)/2329249+1)/29708213026 
((10^1699*17-53)/20943-1)/4 
((10^1709*106+17)/3-1)/82 
((10^1716*19-1)/773757+1)/94740004 
((10^1727*46-1)/9-1)/82223670 
((10^1731-1)*911/999+10^1731)/273 
((10^1742*5+31)/1262187+1)/6534662 
((10^1746*83-101)/9+1)/423284 
((10^1841*79-7)/340407-1)/233854 
((10^1864*5-41)/790401339-1)/57980 
((10^1872*46+53)/4257-1)/33293740741674252 
((10^1907*52-43)/2825054631+1)/95743456284 
((10^1930-1)/3+10^1930*410)/10186163 
((10^1938*403-43)/9-1)/268450910052 
((10^1992*53-791)/9+1)/9009246 
((117^919+919^117)/423628-1)/5590446 
((12^911+1)^2-2)/23602615806575407 
((139^794+794^139)/18945-1)/259177880 
((17239^449-1)/17238+1)/6 
((17^1395*5-1)/635752046508-1)/92014 
((17^1438*20+1)/1098987-1)/451778 
((17^1505*15-1)/2586395157739267814-1)/60 
((17^1562*3-1)/47296782852070432918+1)/204 
((2^5480*125-1)/15469-1)/112001010 
((2^5592*183+1)/1017756034007+1)/1802064888 
((2^5631*161+1)/21614858257-1)/27434096 
((2^5696*137+1)/2116071-1)/3258302 
((2^5730*183+1)/9910277767-1)/36237714 
((2^5761*199+1)/2193303-1)/978 
((2^5835*73-1)/670391-1)/32726264 
((2^5902*69+1)/73-1)/85211832 
((2^5930*193-1)/6956802429+1)/1580 
((2^5964*127-1)/26916772743-1)/232 
((2^6055*9-1)/1290060103-1)/588015508808 
((2^6056*95+1)/259775367-1)/7092334 
((2^6090*57-1)/203+1)/41630 
((2^6151*63-1)/49803415643-1)/2241780 
((2^6258*59-1)/2585+1)/86156391432 
((2^6338*43-1)/11320285671+1)/3918 
((2^6369*145+1)/8522863594867449+1)/190 
((2^6392*6393-1)/22625351+1)/28562375086 
((2^6498*115+1)/2299846117+1)/125834733726 
((2^6579*147-1)/10585-1)/1490 
((2^6591*6590-1)/3173061-1)/88416238702 
((2^6616*11-1)/35+1)/18978 
((3^2424*2^2423)^1+1)/11 
((3^2492*2^2491)^1+1)/4409 
((40^1148+1148^40)/2^80/105649+1)/3572330250 
((555^701-701^555)*2-1)/379916187233 
((6^2150-1)*2/5+3)/14879 
((6^2152-1)*2/5+3)/139 
((6^2157-1)*2/5+3)/257611 
((6^2159-1)*2/5+3)/435443 
((709^683-1)/488400348-1)/8278314231120 
((798^593-1)/797+1)/482578228

These are a bit too complex and few in number to be worth modifying my program for.

Here are numbers to check when k and/or d are 1:

Code:

(10^1796*1-97)/3 -
(1153^563*1-1)/1152 -
(11^1589*1+10)/111 +
(11^1907*1-1)/10 -
(12739^449*1-1)/12738 -
(14969^449*1-1)/14968 -
(1531^593*1-1)/1530 -
(17239^449*1-1)/17238 -
(20^1487*1-1)/19 -
(2241^127*1-1)/2240 -
(2285^127*1-1)/2284 -
(2324^127*1-1)/2323 -
(271^709*1-1)/270 -
(3079^463*1-1)/3078 -
(3352403^257*1-1)/3352402 -
(3461^479*1-1)/3460 -
(3919^499*1-1)/3918 -
(3^4033*1+2)/25 +
(3^4153*1+2)/25 +
(4451^463*1-1)/4450 -
(4801^439*1-1)/4800 -
(4801^463*1-1)/4800 -
(4831^487*1-1)/4830 -
(500^683*1-1)/499 -
(5657^457*1-1)/5656 -
(5689^439*1-1)/5688 -
(6011^499*1-1)/6010 -
(605^605*1+604)/365421 +
(6121^443*1-1)/6120 -
(6173^467*1-1)/6172 -
(6197^439*1-1)/6196 -
(644^613*1-1)/643 -
(665^631*1-1)/664 -
(6^2496*1-11)/5 +
(705669073^223*1-1)/705669072 -
(7213^461*1-1)/7212 -
(7307^479*1-1)/7306 -
(732^661*1-1)/731 -
(8059^431*1-1)/8058 -
(853^619*1-1)/852 -
(902^563*1-1)/901 -
(9491^479*1-1)/9490 -
(9587^457*1-1)/9586 -
(19^1422*1+18)/1 +
(22^1248*1+21)/1 +
(23^1390*1+22)/1 +
(24^1194*1-23)/1 -
(24^1404*1-23)/1 -
(28^1279*1+27)/1 +
(2^5392*1+63)/1 +
(2^5484*1+63)/1 +
(2^5517*1-63)/1 -
(2^5547*1+3)/1 -
(2^5547*1+3)/1 +
(2^5567*1+9)/1 -
(2^5586*1-17)/1 +
(2^5588*1+127)/1 +
(2^5607*1+65)/1 -
(2^5678*1-33)/1 +
(2^5742*1+255)/1 +
(2^5904*1-17)/1 +
(2^5955*1+255)/1 +
(2^6017*1-15)/1 -
(2^6136*1-63)/1 -
(2^6147*1+1025)/1 -
(2^6174*1+2049)/1 -
(2^6338*1-33)/1 +
(2^6437*1-31)/1 -
(2^6465*1+1025)/1 -
(2^6495*1+8193)/1 -
(30^1155*1+29)/1 +
(31^1230*1+30)/1 +
(34^1174*1-33)/1 -
(39^1187*1-38)/1 -
(39^1197*1-38)/1 -
(43^1017*1-42)/1 -
(45^1172*1+44)/1 +
(46^1166*1+45)/1 +
(48^1114*1+47)/1 +
(49^1076*1+48)/1 +
(52^939*1+51)/1 +
(69^1034*1+68)/1 +
(70^1021*1-69)/1 -
(70^1030*1+69)/1 +
(72^1054*1-71)/1 -
(605^605*3+2)/1 +

I cover about 80% of prps in short form below 2000 digits.

Can many numbers of the form (x^y*y^x+-f)/d be helped? I believe I could process them but would hardly get any useful results as we don't have factorizations of x^a*y^b+-1. They are about 10% of the total numbers.

henryzz · 2012-02-29, 14:10

I make regex's for some more forms and the last 5% is pretty much rare stuff.
I have attached my list of prps sorted with the forms marked. I can only process forms 1-3.5

henryzz · 2012-03-01, 23:09

What have people checked from the numbers I posted? I can check some more tomorrow.

2012-02-28, 21:18	#67
henryzz Just call me Henry "David" Sep 2007 Cambridge (GMT/BST) 5880₁₀ Posts	Add $ to the end of ^\(([0-9]+)\^([0-9]+)\([0-9]+)([+-])([0-9]+)\)/([0-9]+) to make ^\(([0-9]+)\^([0-9]+)\([0-9]+)([+-])([0-9]+)\)/([0-9]+)$ Otherwise it lets lines like (13^147919-1)/453707218/3^9 (2^543845-1)/16775191/3461^2 through which confuse the program. Last fiddled with by henryzz on 2012-02-28 at 21:19

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2012-02-28, 21:57	#68
henryzz Just call me Henry "David" Sep 2007 Cambridge (GMT/BST) 2³×3×5×7² Posts	The results from running on the first 1000 prps (10^163114-41)/99 - (19^127411-1)/10 - (19^12873+1)/2 + (2^546377-1)/615 - (2^550269-1)/275 - (2^550269-1)/275 N-1 needed help with factors from 2^5500-1 This was the only one that benefitted as all the others had already been found but still don't have a large enough factored part.

2012-02-28, 23:33	#70
firejuggler Apr 2010 Over the rainbow 2³·5²·13 Posts	(10^1728*52-43)/9 done

2012-02-29, 03:20	#71
wblipp "William" May 2003 New Haven 2·7·13² Posts	Great work! Sure beats my manual scans. (2^6481*105-1)/209 - finished.

2012-02-29, 04:23	#72
firejuggler Apr 2010 Over the rainbow A28₁₆ Posts	done a few more

2012-02-29, 05:18	#73
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2·7·677 Posts	Everything base 10 is done long ago at M.Kamada's site. It only needs to be imported.

2012-02-29, 08:58	#74
YuL Feb 2012 Paris, France 7×23 Posts	Nice work henryzz. Done N-1 proof for (2^6140*17-1)/67.

2012-03-01, 23:09	#77
henryzz Just call me Henry "David" Sep 2007 Cambridge (GMT/BST) 2³·3·5·7² Posts	What have people checked from the numbers I posted? I can check some more tomorrow.