Fermat number factors - Page 3

geoff · 2006-11-30, 01:52

Here are some stats for generalised Fermat primes of the form (a*2^m)^8+1 for odd prime powers a < 72.

Citrix · 2006-12-26, 05:43

3^16 should be done to a million by the end of the year. No primes yet. Does anyone want the residues?

geoff · 2006-12-31, 02:48

Quote:

Originally Posted by Citrix

3^16 should be done to a million by the end of the year. No primes yet. Does anyone want the residues?

You could send me a copy if you like, g_w_reynolds at yahoo dot co dot nz.

I'm still slowly testing 5^16 and some others. I have sieved up to 7 trillion and tested up to n=291000 so far, last prime was at n=253376, just shy of the top 5000 list.

Citrix · 2007-01-01, 20:20

Geoff, about 222 candidates are left to be PRPed. Once done I will email you the residues. I would also like to continue to work on 3^16. Do you have any sieved ranges for me?

geoff · 2007-01-03, 00:13

Quote:

Originally Posted by Citrix

Geoff, about 222 candidates are left to be PRPed. Once done I will email you the residues. I would also like to continue to work on 3^16. Do you have any sieved ranges for me?

I have only sieved up to n=1,000,000, but 3^16*2^n+1 with n=8 (mod 16) is still in the sieve if you want to do that sequence? [a.k.a. (9*2^m)^8+1].

Citrix · 2007-01-03, 00:28

I can work on it..., please post the file.
What other k's do you have sieved that are less than 2^31?

edit: I will start sieving 3^16 from 1M onwards.

geoff · 2007-01-03, 00:52

Quote:

Originally Posted by Citrix

I can work on it..., please post the file.
What other k's do you have sieved that are less than 2^31?

None :-) k=17^8 is the next smallest, a little over 2^32. I'll post the sieve file for k=3^16 tomorrow in case you still want it.

The prp tests for the sequences I am sieving, (the largest being k=67^8), dont take any longer than for k=3^16.

geoff · 2007-01-05, 22:15

Attached is the sieve for 3^16*2^n+1 with n=8 (mod 16), 300K < n < 1M.

geoff · 2007-01-08, 06:15

(53*2^37463)^8+1 is prime.

Citrix · 2007-01-16, 07:12

Geoff, I am interested in taking 3^16 a little it higher. Can you new sieve make sieving even faster?

Basically I am trying to find a 1 million bit prime for 3^16 so it can enter the top 20 generalized fermat list.

Thanks!

Citrix · 2007-01-22, 08:34

Geoff, For sieving 3^16 from n=1M to 2M, what version of the program should I use? Is srsieve2.exe faster, or could your write specific code for this series.

Any progress on implementing SPH for 1 k. May be it could be implemented for some of the low primes for factorization of p-1. Say less than 32?

I think we should extend 3^16 to higher n's. It might be a good candidate to extend to 10M digits.

3^16 n=8 (mod 16) series is almsot done to 500K. No primes yet.

2007-01-03, 00:28	#28
Citrix Jun 2003 2·7·113 Posts	I can work on it..., please post the file. What other k's do you have sieved that are less than 2^31? edit: I will start sieving 3^16 from 1M onwards. Last fiddled with by Citrix on 2007-01-03 at 00:29

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2006-11-30, 01:52	#23
geoff Mar 2003 New Zealand 13·89 Posts	Here are some stats for generalised Fermat primes of the form (a*2^m)^8+1 for odd prime powers a < 72.

2006-12-26, 05:43	#24
Citrix Jun 2003 2×7×113 Posts	3^16 should be done to a million by the end of the year. No primes yet. Does anyone want the residues?

2007-01-01, 20:20	#26
Citrix Jun 2003 2·7·113 Posts	Geoff, about 222 candidates are left to be PRPed. Once done I will email you the residues. I would also like to continue to work on 3^16. Do you have any sieved ranges for me?

2007-01-08, 06:15	#31
geoff Mar 2003 New Zealand 13×89 Posts	(53*2^37463)^8+1 is prime.

2007-01-16, 07:12	#32
Citrix Jun 2003 2·7·113 Posts	Geoff, I am interested in taking 3^16 a little it higher. Can you new sieve make sieving even faster? Basically I am trying to find a 1 million bit prime for 3^16 so it can enter the top 20 generalized fermat list. Thanks!

2007-01-22, 08:34	#33
Citrix Jun 2003 2·7·113 Posts	Geoff, For sieving 3^16 from n=1M to 2M, what version of the program should I use? Is srsieve2.exe faster, or could your write specific code for this series. Any progress on implementing SPH for 1 k. May be it could be implemented for some of the low primes for factorization of p-1. Say less than 32? I think we should extend 3^16 to higher n's. It might be a good candidate to extend to 10M digits. 3^16 n=8 (mod 16) series is almsot done to 500K. No primes yet.