"Divides Phi" category - Page 2

Batalov · 2015-06-03, 00:02

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...

paulunderwood · 2019-01-26, 20:16

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!

Batalov · 2019-01-26, 23:54

It's a lot of iron and a good choice of candidates

...and having the DivPhi self-compiled binary.
Put these three together and you got something.

Stargate38 · 2019-01-27, 21:48

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.

Stargate38 · 2019-03-04, 18:58

It's been over a month, and there's been no answer to my question. Where can I get DivPhi?

sweety439 · 2019-03-05, 14:48

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).

Batalov · 2019-03-05, 17:06

Quote:

Originally Posted by sweety439

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).

That is false.

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)

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)

sweety439 · 2019-03-05, 20:46

Quote:

Originally Posted by Batalov

That is false.

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)

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)

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.

sweety439 · 2019-03-05, 20:48

Quote:

Originally Posted by Batalov

That is false.

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)

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)

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?

Batalov · 2019-03-06, 04:23

Quote:

Originally Posted by sweety439

Um... these b's seem to be all primes .....

Wrong again.

Code:

2*695^94625+1 Divides Phi(695^94625/5^4,2) [g427] [268924 digits] L1471 2011

sweety439 · 2019-03-06, 16:04

Quote:

Originally Posted by Batalov

Wrong again.

Code:

2*695^94625+1 Divides Phi(695^94625/5^4,2) [g427] [268924 digits] L1471 2011

This is not "Divides Phi(695^94625,2)", i.e. k*b^n+1 does not divide Phi(b^n,2), and not belong to this category.

2019-01-26, 20:16	#13
paulunderwood Sep 2002 Database er0rr 7233₈ Posts	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! Last fiddled with by paulunderwood on 2019-01-26 at 20:21

2019-03-04, 18:58	#16
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 1010010111₂ Posts	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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2015-06-03, 00:02	#12
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶×13 Posts	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...

2019-01-26, 23:54	#14
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶·13 Posts	It's a lot of iron and a good choice of candidates ...and having the DivPhi self-compiled binary. Put these three together and you got something.

2019-01-27, 21:48	#15
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 3·13·17 Posts	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.