Fermat number factors - Page 2

Citrix · 2006-08-31, 02:01

Thanks for the file. I will probably go to 1M.

I would like to reserve 500-550K also.

geoff · 2006-09-03, 01:45

Citrix · 2006-09-03, 02:40

Code:

Primes
43046721*2^176+1 is prime! 
43046721*2^1792+1 is prime! 
43046721*2^19936+1 is prime! 
43046721*2^87520+1 is prime! 
43046721*2^168480+1 is prime!
43046721*2^360960+1 is prime!

I was expecting a prime there. I think there is a prime if you double the range need to be checked after every prime found.

So I think the next prime will be between 700-750K.

Citrix · 2006-09-04, 06:04

I did some general base fermat search upto n=5000 and k=10000. Here are the results.

9*2^2+1 is a Factor of GF(1,6)!!!! (0.000000 seconds)
9*2^162+1 is a Factor of GF(158,3)!!!! (0.000000 seconds)
9*2^206+1 is a Factor of GF(205,5)!!!! (0.000000 seconds)
25*2^2+1 is a Factor of GF(1,10)!!!! (0.000000 seconds)
25*2^52+1 is a Factor of GF(48,10)!!!! (0.000000 seconds)
49*2^30+1 is a Factor of GF(29,10)!!!! (0.000000 seconds)
49*2^30+1 is a Factor of GF(29,12)!!!! (0.000000 seconds)
81*2^4+1 is a Factor of GF(2,6)!!!! (0.000000 seconds)
81*2^324+1 is a Factor of GF(319,3)!!!! (0.000000 seconds)
361*2^100+1 is a Factor of GF(99,5)!!!! (0.000000 seconds)
841*2^144+1 is a Factor of GF(143,10)!!!! (0.000000 seconds)
2601*2^40+1 is a Factor of GF(35,6)!!!! (0.000000 seconds)
7225*2^202+1 is a Factor of GF(201,6)!!!! (0.000000 seconds)
9*2^1494+1 is a Factor of GF(1488,3)!!!! (0.016000 seconds)
9*2^2826+1 is a Factor of GF(2822,3)!!!! (0.047000 seconds)
9*2^3354+1 is a Factor of GF(3353,10)!!!! (0.187000 seconds)
9*2^3690+1 is a Factor of GF(3684,3)!!!! (0.078000 seconds)
9*2^4842+1 is a Factor of GF(4838,3)!!!! (0.157000 seconds)
25*2^3904+1 is a Factor of GF(3903,6)!!!! (0.281000 seconds)
81*2^1384+1 is a Factor of GF(1379,6)!!!! (0.016000 seconds)
81*2^1384+1 is a Factor of GF(1379,8)!!!! (0.015000 seconds)

BAsed on the results I think it is best to stick under k=100, which prothsearch.net is already searching. So after k=3^16 there is no point working on these numbers.

Citrix · 2006-09-04, 20:24

reserving 550-800K

geoff · 2006-09-10, 00:58

I've finished 300K-400K, no further primes.

geoff · 2006-10-31, 00:36

I have sieved k=3^16 up to p=2.7 trillion, sieve file attached.

I am also sieving k=a^8 where a is a prime power less than 72 (there are 10 such sequences (a*2^m)^8+1 with primes, a<72 is chosen so that a^8 is small enough for LLR to use a zero-padded FFT). I can post sieve files if anyone is interested in these.

Citrix · 2006-10-31, 00:54

3^16 is almost complete till 890K. Continuing till 1M. Thanks for the updated sieve files.

geoff · 2006-11-18, 22:24

Quote:

Originally Posted by Citrix

3^16 is almost complete till 890K. Continuing till 1M. Thanks for the updated sieve files.

Here is the remaining sieve for 890K-1M done up to p=4T.

Citrix · 2006-11-18, 22:33

Please don't sieve further on 3^16 for right now. Ranges are already assigned to computers, there is no way to update them, if new factors are found.

Thanks for the updated file.

geoff · 2006-11-18, 23:11

Quote:

Originally Posted by Citrix

Please don't sieve further on 3^16 for right now. Ranges are already assigned to computers, there is no way to update them, if new factors are found.

OK, good luck. I was sieving 3^16 in a sieve together with other sequences so I didn't spend a lot of extra time on it, but I'll remove it from the sieve now.

2006-09-03, 01:45	#13
geoff Mar 2003 New Zealand 13·89 Posts	(3*2^22560)^16+1 is prime!

2006-09-03, 02:40	#14
Citrix Jun 2003 2·7·113 Posts	Code: Primes 430467212^176+1 is prime! 430467212^1792+1 is prime! 430467212^19936+1 is prime! 430467212^87520+1 is prime! 430467212^168480+1 is prime! 430467212^360960+1 is prime! I was expecting a prime there. I think there is a prime if you double the range need to be checked after every prime found. So I think the next prime will be between 700-750K. Last fiddled with by Citrix on 2006-09-03 at 03:11

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2006-08-31, 02:01	#12
Citrix Jun 2003 11000101110₂ Posts	Thanks for the file. I will probably go to 1M. I would like to reserve 500-550K also.

2006-09-04, 06:04	#15
Citrix Jun 2003 2·7·113 Posts	I did some general base fermat search upto n=5000 and k=10000. Here are the results. 92^2+1 is a Factor of GF(1,6)!!!! (0.000000 seconds) 92^162+1 is a Factor of GF(158,3)!!!! (0.000000 seconds) 92^206+1 is a Factor of GF(205,5)!!!! (0.000000 seconds) 252^2+1 is a Factor of GF(1,10)!!!! (0.000000 seconds) 252^52+1 is a Factor of GF(48,10)!!!! (0.000000 seconds) 492^30+1 is a Factor of GF(29,10)!!!! (0.000000 seconds) 492^30+1 is a Factor of GF(29,12)!!!! (0.000000 seconds) 812^4+1 is a Factor of GF(2,6)!!!! (0.000000 seconds) 812^324+1 is a Factor of GF(319,3)!!!! (0.000000 seconds) 3612^100+1 is a Factor of GF(99,5)!!!! (0.000000 seconds) 8412^144+1 is a Factor of GF(143,10)!!!! (0.000000 seconds) 26012^40+1 is a Factor of GF(35,6)!!!! (0.000000 seconds) 72252^202+1 is a Factor of GF(201,6)!!!! (0.000000 seconds) 92^1494+1 is a Factor of GF(1488,3)!!!! (0.016000 seconds) 92^2826+1 is a Factor of GF(2822,3)!!!! (0.047000 seconds) 92^3354+1 is a Factor of GF(3353,10)!!!! (0.187000 seconds) 92^3690+1 is a Factor of GF(3684,3)!!!! (0.078000 seconds) 92^4842+1 is a Factor of GF(4838,3)!!!! (0.157000 seconds) 252^3904+1 is a Factor of GF(3903,6)!!!! (0.281000 seconds) 812^1384+1 is a Factor of GF(1379,6)!!!! (0.016000 seconds) 81*2^1384+1 is a Factor of GF(1379,8)!!!! (0.015000 seconds) BAsed on the results I think it is best to stick under k=100, which prothsearch.net is already searching. So after k=3^16 there is no point working on these numbers.

2006-09-04, 20:24	#16
Citrix Jun 2003 2·7·113 Posts	reserving 550-800K

2006-09-10, 00:58	#17
geoff Mar 2003 New Zealand 485₁₆ Posts	I've finished 300K-400K, no further primes.

2006-10-31, 00:54	#19
Citrix Jun 2003 2×7×113 Posts	3^16 is almost complete till 890K. Continuing till 1M. Thanks for the updated sieve files.

2006-11-18, 22:33	#21
Citrix Jun 2003 1582₁₀ Posts	Please don't sieve further on 3^16 for right now. Ranges are already assigned to computers, there is no way to update them, if new factors are found. Thanks for the updated file.