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 015
Code:
MM(31) has 1 factors in range k = [0, 16336320], passes 015
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.