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2020-11-27, 14:13   #12
kriesel

"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

114538 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