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After the recent George's fix to the foundation (which allows choosing fast special FFT where available, much faster than a general mod), the search for a 2*67607^n+1 prime (and a likely Divides Phi entry) is now possible once again! I'll give it a shot, maybe...
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I have observed a slew of "Divides Phi" mega-primes being submitted. Are these easy to find or are these due to a lot of crunching?
Edit: Congratulations! |
It's a lot of iron and a good choice of candidates :rolleyes:
...and having the DivPhi self-compiled binary. Put these three together and you got something. |
Any chance you could tell me how/where to get that DivPhi binary, or at least its source code? I would love to crunch some of those numbers myself. Just something to do when I'm not running factorizations.
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I really want to download that program of yours.
It's been over a month, and there's been no answer to my question. Where can I get DivPhi?
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1 Attachment(s)
all n's and k's are written in duodecimal, only consider n ends with E (i.e. n = 11 mod 12), searched to duodecimal 1000 (decimal 1728).
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[QUOTE=sweety439;510169]all n's and k's are written in duodecimal, only consider n ends with E (i.e. n = 11 mod 12), searched to duodecimal 1000 (decimal 1728).[/QUOTE]
[COLOR="Red"]That is false. [/COLOR] [CODE]----- -------------------------------- ------- ----- ---- -------------- rank description digits who year comment ----- -------------------------------- ------- ----- ---- -------------- 46623 2*3^152529+1 72776 gb 2000 Divides Phi(3^152528,2) 88279 2*3^6225+1 2971 C 1992 Divides Phi(3^6223,2) 94491 2*3^4217+1 2013 C 1992 Divides Phi(3^4217,2) [/CODE] And what about these examples? [CODE]----- -------------------------------- ------- ----- ---- -------------- rank description digits who year comment ----- -------------------------------- ------- ----- ---- -------------- 46760 10*79^37853+1 71832 p67 2005 Divides Phi(79^37853,2) 47960 6*31^43640+1 65084 p67 2004 Divides Phi(31^43640,2) 47983 22*5^93078+1 65061 p67 2004 Divides Phi(5^93077,2) 49755 10*7^70115+1 59256 p67 2004 Divides Phi(7^70114,2) 58087 72*7^40122+1 33909 g151 2002 Divides Phi(7^40121,2) 62022 10*79^15023+1 28510 g255 2003 Divides Phi(79^15023,2) 63201 10*7^29447+1 24887 g151 2000 Divides Phi(7^29446,2) 73588 6*19^8776+1 11224 gk 1999 Divides Phi(19^8776,2) 73855 10*43^6569+1 10732 g154 1999 Divides Phi(43^6569,2) 75051 6*17^7717+1 9497 gk 1999 Divides Phi(17^7717,2) 75656 38*5^12727+1 8898 gk 2000 Divides Phi(5^12727,2) 77176 8*29^5189+1 7590 gk 2000 Divides Phi(29^5189,2) 81124 40*19^4531+1 5796 gk 1999 Divides Phi(19^4531,2) 92326 10*10111^551+1 2208 g141 1999 Divides Phi(10111^551,2) 96820 10*10111^431+1 1728 g141 1999 Divides Phi(10111^431,2) 97115 30*7^1944+1 1645 K 1994 Divides Phi(7^1944,2) 97376 30*11^1514+1 1579 K 1994 Divides Phi(11^1514,2) 97522 30*19^1210+1 1549 K 1994 Divides Phi(19^1210,2) 98309 16*13^1309+1 1460 K 1994 Divides Phi(13^1309,2) 102020 40*29^886+1 1298 K 1994 Divides Phi(29^886,2) 102436 24*19^1005+1 1287 K 1994 Divides Phi(19^1005,2) 106355 30*13^1074+1 1198 K 1994 Divides Phi(13^1074,2) 118605 26*3^2121+1 1014 K 1994 Divides Phi(3^2121,2) 118738 8*29^689+1 1009 K 1994 Divides Phi(29^689,2) [/CODE] |
2 Attachment(s)
[QUOTE=Batalov;510184][COLOR="Red"]That is false. [/COLOR]
[CODE]----- -------------------------------- ------- ----- ---- -------------- rank description digits who year comment ----- -------------------------------- ------- ----- ---- -------------- 46623 2*3^152529+1 72776 gb 2000 Divides Phi(3^152528,2) 88279 2*3^6225+1 2971 C 1992 Divides Phi(3^6223,2) 94491 2*3^4217+1 2013 C 1992 Divides Phi(3^4217,2) [/CODE] And what about these examples? [CODE]----- -------------------------------- ------- ----- ---- -------------- rank description digits who year comment ----- -------------------------------- ------- ----- ---- -------------- 46760 10*79^37853+1 71832 p67 2005 Divides Phi(79^37853,2) 47960 6*31^43640+1 65084 p67 2004 Divides Phi(31^43640,2) 47983 22*5^93078+1 65061 p67 2004 Divides Phi(5^93077,2) 49755 10*7^70115+1 59256 p67 2004 Divides Phi(7^70114,2) 58087 72*7^40122+1 33909 g151 2002 Divides Phi(7^40121,2) 62022 10*79^15023+1 28510 g255 2003 Divides Phi(79^15023,2) 63201 10*7^29447+1 24887 g151 2000 Divides Phi(7^29446,2) 73588 6*19^8776+1 11224 gk 1999 Divides Phi(19^8776,2) 73855 10*43^6569+1 10732 g154 1999 Divides Phi(43^6569,2) 75051 6*17^7717+1 9497 gk 1999 Divides Phi(17^7717,2) 75656 38*5^12727+1 8898 gk 2000 Divides Phi(5^12727,2) 77176 8*29^5189+1 7590 gk 2000 Divides Phi(29^5189,2) 81124 40*19^4531+1 5796 gk 1999 Divides Phi(19^4531,2) 92326 10*10111^551+1 2208 g141 1999 Divides Phi(10111^551,2) 96820 10*10111^431+1 1728 g141 1999 Divides Phi(10111^431,2) 97115 30*7^1944+1 1645 K 1994 Divides Phi(7^1944,2) 97376 30*11^1514+1 1579 K 1994 Divides Phi(11^1514,2) 97522 30*19^1210+1 1549 K 1994 Divides Phi(19^1210,2) 98309 16*13^1309+1 1460 K 1994 Divides Phi(13^1309,2) 102020 40*29^886+1 1298 K 1994 Divides Phi(29^886,2) 102436 24*19^1005+1 1287 K 1994 Divides Phi(19^1005,2) 106355 30*13^1074+1 1198 K 1994 Divides Phi(13^1074,2) 118605 26*3^2121+1 1014 K 1994 Divides Phi(3^2121,2) 118738 8*29^689+1 1009 K 1994 Divides Phi(29^689,2) [/CODE][/QUOTE] Well, I am already searched 2*n^k+1 and 2*n^k-1 for all bases n up to duodecimal 1000 (decimal 1728), and the exponent k are also searched to k=duodecimal 1000 (decimal 1728), there are only few bases n<=1000 (decimal 1728) without primes of the form 2*n^k+1 or 2*n^k-1 with k<=1000 (decimal 1728), these are the two text files, if you want it. Note: all the n's and k's in these two text files are written in duodecimal, and for 2*n^k+1, if n=1 (mod 3), then all numbers of the form 2*n^k+1 are divisible by 3, thus, I didn't search 2*n^k+1 for n=1 (mod 3), i.e. n ends with 1, 4, 7, or X in duodecimal. |
[QUOTE=Batalov;510184][COLOR="Red"]That is false. [/COLOR]
[CODE]----- -------------------------------- ------- ----- ---- -------------- rank description digits who year comment ----- -------------------------------- ------- ----- ---- -------------- 46623 2*3^152529+1 72776 gb 2000 Divides Phi(3^152528,2) 88279 2*3^6225+1 2971 C 1992 Divides Phi(3^6223,2) 94491 2*3^4217+1 2013 C 1992 Divides Phi(3^4217,2) [/CODE] And what about these examples? [CODE]----- -------------------------------- ------- ----- ---- -------------- rank description digits who year comment ----- -------------------------------- ------- ----- ---- -------------- 46760 10*79^37853+1 71832 p67 2005 Divides Phi(79^37853,2) 47960 6*31^43640+1 65084 p67 2004 Divides Phi(31^43640,2) 47983 22*5^93078+1 65061 p67 2004 Divides Phi(5^93077,2) 49755 10*7^70115+1 59256 p67 2004 Divides Phi(7^70114,2) 58087 72*7^40122+1 33909 g151 2002 Divides Phi(7^40121,2) 62022 10*79^15023+1 28510 g255 2003 Divides Phi(79^15023,2) 63201 10*7^29447+1 24887 g151 2000 Divides Phi(7^29446,2) 73588 6*19^8776+1 11224 gk 1999 Divides Phi(19^8776,2) 73855 10*43^6569+1 10732 g154 1999 Divides Phi(43^6569,2) 75051 6*17^7717+1 9497 gk 1999 Divides Phi(17^7717,2) 75656 38*5^12727+1 8898 gk 2000 Divides Phi(5^12727,2) 77176 8*29^5189+1 7590 gk 2000 Divides Phi(29^5189,2) 81124 40*19^4531+1 5796 gk 1999 Divides Phi(19^4531,2) 92326 10*10111^551+1 2208 g141 1999 Divides Phi(10111^551,2) 96820 10*10111^431+1 1728 g141 1999 Divides Phi(10111^431,2) 97115 30*7^1944+1 1645 K 1994 Divides Phi(7^1944,2) 97376 30*11^1514+1 1579 K 1994 Divides Phi(11^1514,2) 97522 30*19^1210+1 1549 K 1994 Divides Phi(19^1210,2) 98309 16*13^1309+1 1460 K 1994 Divides Phi(13^1309,2) 102020 40*29^886+1 1298 K 1994 Divides Phi(29^886,2) 102436 24*19^1005+1 1287 K 1994 Divides Phi(19^1005,2) 106355 30*13^1074+1 1198 K 1994 Divides Phi(13^1074,2) 118605 26*3^2121+1 1014 K 1994 Divides Phi(3^2121,2) 118738 8*29^689+1 1009 K 1994 Divides Phi(29^689,2) [/CODE][/QUOTE] Um... Currently I know what you means, not only 2*b^n+1 with b ends with E in duodecimal, but also some numbers k*b^n+1 with k>2 also divides Phi(b^n,2) ... but these b's seem to be all primes ...... of course since gcd(k+1,b-1) must be 1 and b is prime > 2 (thus odd), thus these k's must be even ... but are there any k=4 primes? |
[QUOTE=sweety439;510197]Um... these b's seem to be all primes .....[/QUOTE]
Wrong again. [CODE]2*695^94625+1 Divides Phi(695^94625/5^4,2) [g427] [268924 digits] L1471 2011 [/CODE] |
[QUOTE=Batalov;510220]Wrong again.
[CODE]2*695^94625+1 Divides Phi([B]695^94625/5^4[/B],2) [g427] [268924 digits] L1471 2011 [/CODE][/QUOTE] This is not "Divides Phi([B]695^94625[/B],2)", i.e. k*b^n+1 does not divide Phi(b^n,2), and not belong to this category. |
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