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Checked upto 250K. Extending. I found PFGW to be faster than alpertron's program. Also I think PFGW uses the same code that Prime95 uses, so it is real fast.
Citrix |
[code]
pfgw -l -f100 -j452929 pfgw -l -f100 -j453962 pfgw -l -f100 -j458329 pfgw -l -f100 -j458882 pfgw -l -f100 -j466489 pfgw -l -f100 -j474338 pfgw -l -f100 -j477481 pfgw -l -f100 -j482162 pfgw -l -f100 -j491401 pfgw -l -f100 -j493039 pfgw -l -f100 -j498002 pfgw -l -f100 -j502681 pfgw -l -f100 -j506018 pfgw -l -f100 -j516961 pfgw -l -f100 -j518162 pfgw -l -f100 -j528529 pfgw -l -f100 -j531441 pfgw -l -f100 -j537289 pfgw -l -f100 -j542882 pfgw -l -f100 -j546121 pfgw -l -f100 -j547058 pfgw -l -f100 -j552049 pfgw -l -f100 -j559682 pfgw -l -f100 -j564001 pfgw -l -f100 -j571787 pfgw -l -f100 -j573049 pfgw -l -f100 -j579121 pfgw -l -f100 -j585362 pfgw -l -f100 -j591361 pfgw -l -f100 -j597529 pfgw -l -f100 -j598418 pfgw -l -f100 -j601526 pfgw -l -f100 -j619369 pfgw -l -f100 -j620498 pfgw -l -f100 -j633938 pfgw -l -f100 -j635209 pfgw -l -f100 -j647522 pfgw -l -f100 -j652082 pfgw -l -f100 -j654481 pfgw -l -f100 -j657721 pfgw -l -f100 -j665858 pfgw -l -f100 -j674041 pfgw -l -f100 -j677329 pfgw -l -f100 -j683929 pfgw -l -f100 -j687241 pfgw -l -f100 -j689138 pfgw -l -f100 -j703298 pfgw -l -f100 -j703921 pfgw -l -f100 -j704969 pfgw -l -f100 -j707281 pfgw -l -f100 -j715822 pfgw -l -f100 -j717602 pfgw -l -f100 -j722402 pfgw -l -f100 -j727609 pfgw -l -f100 -j734449 pfgw -l -f100 -j736898 pfgw -l -f100 -j737881 pfgw -l -f100 -j742586 pfgw -l -f100 -j744769 pfgw -l -f100 -j751538 pfgw -l -f100 -j761378 pfgw -l -f100 -j766322 pfgw -l -f100 -j769129 pfgw -l -f100 -j776161 pfgw -l -f100 -j778034 pfgw -l -f100 -j779689 pfgw -l -f100 -j781250 pfgw -l -f100 -j786769 pfgw -l -f100 -j796322 pfgw -l -f100 -j821762 pfgw -l -f100 -j822649 pfgw -l -f100 -j823543 pfgw -l -f100 -j826898 pfgw -l -f100 -j829921 pfgw -l -f100 -j837218 pfgw -l -f100 -j844561 pfgw -l -f100 -j852818 pfgw -l -f100 -j863041 pfgw -l -f100 -j868562 pfgw -l -f100 -j873842 pfgw -l -f100 -j877969 pfgw -l -f100 -j885481 pfgw -l -f100 -j896809 pfgw -l -f100 -j905858 pfgw -l -f100 -j908209 pfgw -l -f100 -j912673 pfgw -l -f100 -j916658 pfgw -l -f100 -j923521 pfgw -l -f100 -j932978 pfgw -l -f100 -j935089 pfgw -l -f100 -j942841 pfgw -l -f100 -j954529 pfgw -l -f100 -j954962 pfgw -l -f100 -j966289 pfgw -l -f100 -j982081 pfgw -l -f100 -j982802 pfgw -l -f100 -j986078 pfgw -l -f100 -j994009 pfgw -l -f100 -j1005362 pfgw -l -f100 -j1018081 pfgw -l -f100 -j1026169 pfgw -l -f100 -j1030301 pfgw -l -f100 -j1033922 pfgw -l -f100 -j1038361 pfgw -l -f100 -j1042441 pfgw -l -f100 -j1057058 pfgw -l -f100 -j1062882 pfgw -l -f100 -j1062961 pfgw -l -f100 -j1067089 pfgw -l -f100 -j1074578 pfgw -l -f100 -j1079521 pfgw -l -f100 -j1092242 pfgw -l -f100 -j1092727 pfgw -l -f100 -j1100401 pfgw -l -f100 -j1104098 pfgw -l -f100 -j1104601 pfgw -l -f100 -j1125721 pfgw -l -f100 -j1128002 pfgw -l -f100 -j1129969 pfgw -l -f100 -j1142761 pfgw -l -f100 -j1143574 pfgw -l -f100 -j1146098 pfgw -l -f100 -j1158242 pfgw -l -f100 -j1181569 pfgw -l -f100 -j1182722 pfgw -l -f100 -j1190281 pfgw -l -f100 -j1194649 pfgw -l -f100 -j1195058 pfgw -l -f100 -j1203409 pfgw -l -f100 -j1216609 pfgw -l -f100 -j1225043 pfgw -l -f100 -j1229881 pfgw -l -f100 -j1238738 pfgw -l -f100 -j1247689 pfgw -l -f100 -j1261129 pfgw -l -f100 -j1270418 pfgw -l -f100 -j1274641 pfgw -l -f100 -j1295029 pfgw -l -f100 -j1308962 pfgw -l -f100 -j1315442 pfgw -l -f100 -j1324801 pfgw -l -f100 -j1329409 pfgw -l -f100 -j1348082 pfgw -l -f100 -j1352569 pfgw -l -f100 -j1354658 pfgw -l -f100 -j1367858 pfgw -l -f100 -j1371241 pfgw -l -f100 -j1374482 pfgw -l -f100 -j1394761 pfgw -l -f100 -j1407842 pfgw -l -f100 -j1408969 pfgw -l -f100 -j1409938 pfgw -l -f100 -j1414562 pfgw -l -f100 -j1419857 pfgw -l -f100 -j1423249 pfgw -l -f100 -j1442401 pfgw -l -f100 -j1442897 pfgw -l -f100 -j1455218 pfgw -l -f100 -j1468898 pfgw -l -f100 -j1471369 pfgw -l -f100 -j1475762 pfgw -l -f100 -j1481089 pfgw -l -f100 -j1489538 pfgw -l -f100 -j1495729 pfgw -l -f100 -j1510441 pfgw -l -f100 -j1515361 pfgw -l -f100 -j1530169 pfgw -l -f100 -j1538258 pfgw -l -f100 -j1552322 pfgw -l -f100 -j1559378 pfgw -l -f100 -j1560001 pfgw -l -f100 -j1573538 pfgw -l -f100 -j1585081 pfgw -l -f100 -j1594323 pfgw -l -f100 -j1630729 pfgw -l -f100 -j1635841 pfgw -l -f100 -j1645298 pfgw -l -f100 -j1646089 pfgw -l -f100 -j1647086 pfgw -l -f100 -j1659842 pfgw -l -f100 -j1661521 pfgw -l -f100 -j1666681 pfgw -l -f100 -j1682209 pfgw -l -f100 -j1689122 pfgw -l -f100 -j1692601 pfgw -l -f100 -j1697809 pfgw -l -f100 -j1708249 pfgw -l -f100 -j1726082 pfgw -l -f100 -j1739761 pfgw -l -f100 -j1745041 pfgw -l -f100 -j1755938 pfgw -l -f100 -j1760929 pfgw -l -f100 -j1770962 pfgw -l -f100 -j1771561 pfgw -l -f100 -j1793618 pfgw -l -f100 -j1816418 pfgw -l -f100 -j1825346 pfgw -l -f100 -j1847042 pfgw -l -f100 -j1852321 pfgw -l -f100 -j1868689 pfgw -l -f100 -j1870178 pfgw -l -f100 -j1874161 pfgw -l -f100 -j1885129 pfgw -l -f100 -j1885682 pfgw -l -f100 -j1907161 pfgw -l -f100 -j1909058 pfgw -l -f100 -j1932578 pfgw -l -f100 -j1953125 pfgw -l -f100 -j1957201 pfgw -l -f100 -j1964162 pfgw -l -f100 -j1985281 pfgw -l -f100 -j1988018 pfgw -l -f100 -j2036162 pfgw -l -f100 -j2052338 pfgw -l -f100 -j2060602 pfgw -l -f100 -j2076722 pfgw -l -f100 -j2084882 pfgw -l -f100 -j2125922 pfgw -l -f100 -j2134178 pfgw -l -f100 -j2159042 pfgw -l -f100 -j2185454 pfgw -l -f100 -j2200802 pfgw -l -f100 -j2209202 pfgw -l -f100 -j2251442 pfgw -l -f100 -j2259938 pfgw -l -f100 -j2285522 pfgw -l -f100 -j2363138 pfgw -l -f100 -j2380562 pfgw -l -f100 -j2389298 pfgw -l -f100 -j2406818 pfgw -l -f100 -j2433218 pfgw -l -f100 -j2450086 pfgw -l -f100 -j2459762 pfgw -l -f100 -j2495378 pfgw -l -f100 -j2522258 pfgw -l -f100 -j2549282 pfgw -l -f100 -j2590058 pfgw -l -f100 -j2649602 pfgw -l -f100 -j2658818 pfgw -l -f100 -j2705138 pfgw -l -f100 -j2742482 pfgw -l -f100 -j2789522 pfgw -l -f100 -j2817938 pfgw -l -f100 -j2839714 pfgw -l -f100 -j2846498 pfgw -l -f100 -j2884802 pfgw -l -f100 -j2885794 pfgw -l -f100 -j2942738 pfgw -l -f100 -j2962178 pfgw -l -f100 -j2991458 pfgw -l -f100 -j3020882 pfgw -l -f100 -j3030722 pfgw -l -f100 -j3060338 pfgw -l -f100 -j3120002 pfgw -l -f100 -j3170162 pfgw -l -f100 -j3188646 pfgw -l -f100 -j3261458 pfgw -l -f100 -j3271682 pfgw -l -f100 -j3292178 pfgw -l -f100 -j3323042 pfgw -l -f100 -j3333362 pfgw -l -f100 -j3364418 pfgw -l -f100 -j3385202 pfgw -l -f100 -j3395618 pfgw -l -f100 -j3416498 pfgw -l -f100 -j3479522 pfgw -l -f100 -j3490082 pfgw -l -f100 -j3521858 pfgw -l -f100 -j3543122 pfgw -l -f100 -j3704642 pfgw -l -f100 -j3737378 pfgw -l -f100 -j3748322 pfgw -l -f100 -j3770258 pfgw -l -f100 -j3814322 pfgw -l -f100 -j3906250 pfgw -l -f100 -j3914402 pfgw -l -f100 -j3970562 [/code] I have completed to 450K. No primes. The above need to be run thorugh PFGW. I cannot do this alone, if some one wants to help me, they can post below and reserve lines. 277 candidates left. If anyone wants residues or factors below 450K let me know. Citrix |
My program is fast for small values of the exponent, say less than 1000. Otherwise you need a program that uses FFT multiplications.
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I have checked upto 2^25000 for primes of the form phi(2^x*p^y,2) for prime p.
These are the PRP I found. Phi(56,2) is 3-PRP! (0.000000 seconds) Phi(80,2) is 3-PRP! (0.000000 seconds) Phi(184,2) is 3-PRP! (0.000000 seconds) Phi(192,2) is 3-PRP! (0.000000 seconds) Phi(208,2) is 3-PRP! (0.000000 seconds) Phi(296,2) is 3-PRP! (0.000000 seconds) Phi(712,2) is 3-PRP! (0.000000 seconds) Phi(1192,2) is 3-PRP! (0.000000 seconds) Phi(1384,2) is 3-PRP! (0.000000 seconds) Phi(1600,2) is 3-PRP! (0.000000 seconds) Phi(2008,2) is 3-PRP! (0.000000 seconds) Phi(2456,2) is 3-PRP! (0.000000 seconds) Phi(2536,2) is 3-PRP! (0.000000 seconds) Phi(7648,2) is 3-PRP! (0.062000 seconds) I am extending the search for p=3. Rest of the p are open for others. Citrix |
[QUOTE=alpertron]It would be better to change the program first to perform trial division only with the candidates that are congruent to 1 or 7 (mod 8) so it will tun twice as fast. I didn't have time to perform the change and upload the new version.[/QUOTE]
Does it work for every phi(n,2)? Luigi |
[QUOTE=Citrix]I have checked upto 2^25000 for primes of the form phi(2^x*p^y,2) for prime p.
These are the PRP I found. Phi(56,2) is 3-PRP! (0.000000 seconds) Phi(80,2) is 3-PRP! (0.000000 seconds) Phi(184,2) is 3-PRP! (0.000000 seconds) Phi(192,2) is 3-PRP! (0.000000 seconds) Phi(208,2) is 3-PRP! (0.000000 seconds) Phi(296,2) is 3-PRP! (0.000000 seconds) Phi(712,2) is 3-PRP! (0.000000 seconds) Phi(1192,2) is 3-PRP! (0.000000 seconds) Phi(1384,2) is 3-PRP! (0.000000 seconds) Phi(1600,2) is 3-PRP! (0.000000 seconds) Phi(2008,2) is 3-PRP! (0.000000 seconds) Phi(2456,2) is 3-PRP! (0.000000 seconds) Phi(2536,2) is 3-PRP! (0.000000 seconds) Phi(7648,2) is 3-PRP! (0.062000 seconds) I am extending the search for p=3. Rest of the p are open for others. Citrix[/QUOTE] How do you define x and y? |
[QUOTE=fetofs]How do you define x and y?[/QUOTE]
x and y are positive integers. Citrix |
[QUOTE=Citrix]I have checked upto 2^25000 for primes of the form phi(2^x*p^y,2) for prime p.
These are the PRP I found. ... I am extending the search for p=3. Rest of the p are open for others. Citrix[/QUOTE] You're re-tracing very old steps. e.g. Yves Gallot found and proved many Phi(n,2) about 5 or so years ago. |
[QUOTE=ET_]Does it work for every phi(n,2)?
Luigi[/QUOTE] For [tex]n[/tex] odd let [tex]N = 2^n-1[/tex] and [tex]x = 2^{(n+1)/2}[/tex] so [tex]x^2 = 2^{n+1} = 2N + 2 \eq 2 \pmod{N}[/tex] This means that for every prime factor of N there is an x such that [tex]x^2\eq 2[/tex]. By the quadratic reciprocity law the values of p are restricted to be of the form [tex]p\eq 1\pmod {8}[/tex] or [tex]p\eq 7\pmod {8}[/tex] |
[QUOTE=alpertron]For [tex]n[/tex] odd let
[tex]N = 2^n-1[/tex] and [tex]x = 2^{(n+1)/2}[/tex] so [tex]x^2 = 2^{n+1} = 2N + 2 \eq 2 \pmod{N}[/tex] This means that for every prime factor of N there is an x such that [tex]x^2\eq 2[/tex]. By the quadratic reciprocity law the values of p are restricted to be of the form [tex]p\eq 1\pmod {8}[/tex] or [tex]p\eq 7\pmod {8}[/tex][/QUOTE] Thank you Dario! :bow: :bow: :bow: Luigi |
[QUOTE=T.Rex]Hi Alperton,
In the second table, you improved the results of Saouter ! Congratulations ! (If Mr Saouter found factors before you, perhaps you should add his name in the tables.) I see that you have found no factors when n=10, 13, 15, 18, ... Maybe these numbers are primes ?! Regards, Tony[/QUOTE]Using my program I've just found that [tex]35198840558 * 3^{14} + 1 = 168354963224856703[/tex] is a prime divisor of [tex]4^{3^{13}}\,+\,2^{3^{13}}\,+\,1[/tex]. |
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