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2020-11-27, 14:13   #12
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

10011001110012 Posts

Quote:
 Originally Posted by piforbreakfast Well dangit, I didn't notice this tidbit until just now. M31 was in fact the exponent I was wanting to test.
FOUR known factors, known for 15 to 39 years. Mfactor can find the smallest in under a minute on one core of an old slow Xeon E5645.
Code:
Searching in the interval k=[0, 16336320]
Each of  16 (p mod 60) passes will consist of 1 intervals of length 272272

Factor with k = 68745. This factor is a probable prime.
MM(31) has 1 factors in range k = [0, 16336320], passes 0-15
Code:
MM(31) has 1 factors in range k = [0, 16336320], passes 0-15
Performed 505654 trial divides
Clocks = 00:00:54.206
Excerpt from http://www.doublemersennes.org/history.php:
Code:
M( M( 31 ) )C: 295257526626031          # k = 68745, Wilfrid Keller 1981 Nov 27
M( M( 31 ) )C: 87054709261955177        # k = 20269004, Tony Forbes - Wilfrid Keller 1994 Aug 20
M( M( 31 ) )C: 242557615644693265201    # k = 56474845800, Reto Keiser  1999 Dec 6
M( M( 31 ) )C: 178021379228511215367151 # k = 41448832329225, Ernst Mayer 2005 June 20
Coincidentally, today is the 39th anniversary of the smallest factor's discovery.
That was just a few months after the beginning of commercial sale of the original IBM PC; several years before the beginning of creation of http. So news of it would have spread by number theory mailing lists.

Last fiddled with by kriesel on 2020-11-27 at 14:32

2020-11-27, 14:30   #13
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

7×19×37 Posts

Quote:
 Originally Posted by piforbreakfast I downloaded the zip file and unpacked the program but absolutely nothing is happening when I try to run it. Is there something else I need to do? The exponent in question is prime. I don't have mfaktc or mlucas installed but would very much like to know where to find those programs.
Climbing the learning curve can provide many hours of enjoyable distraction.
Start through https://www.mersenneforum.org/showthread.php?t=24607. Bookmark it for later reference.
For software after you've absorbed the contents of the first several links there, see http://www.mersenneforum.org/showpos...91&postcount=2 and its attachment.

I'll put up a version of Mfactor later. People really should use and recommend Mfactor, not Factor5. Speed penalty ~7+ measured for Factor5.

Last fiddled with by kriesel on 2020-11-27 at 14:42

2020-11-27, 17:35   #14
ET_
Banned

"Luigi"
Aug 2002
Team Italia

2·74 Posts

Quote:
 Originally Posted by kriesel I'll put up a version of Mfactor later. People really should use and recommend Mfactor, not Factor5. Speed penalty ~7+ measured for Factor5.
I'm the author of Factor5. It was done by joke, and with the purpose to learn how to write a factorization program. It uses full GMP libraries, with no fancy optimization, and still can use up to 16 threads.

Oh, and can work on exponents whose size is only limited by the memory of your computer.

Yep, I'm proud of it, it's my baby...

Luigi

 2020-11-27, 18:20 #15 kriesel     "TF79LL86GIMPS96gpu17" Mar 2017 US midwest 7·19·37 Posts Just to be clear, all functional GIMPS software contributions and their authors are welcome and respected. Cllucas used to be the best primality testing software for Mersennes on OpenCL. Eventually it was eclipsed by Gpuowl. I had written a combined TF and LL test program for x86 on DOS, doing it all integer and without the benefit of some number theory understanding; trial long division and grammar school squaring, in Fortran and then C. Single threaded, but didn't matter way back then when dual processor systems were rare. The run time scaling was absolutely dreadful (higher than cube of exponent), and made clear that better algorithms and better implementation were both required to have any chance. I learned of prime95 and its fft based multiplication in mid 1996, after beginning to implement Karatsuba. It didn't take long to decide to switch to George's far superior program. Last fiddled with by kriesel on 2020-11-27 at 18:26

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