News - January 2011

January 25, 2011

2011^64+1150^64: 262428378691151920451118182145223566271724639692992641
This factor (54 digits) was found by P-1 (using B1 = 1e9) in step 1, since
262428378691151920451118182145223566271724639692992641 - 1 = 2^7.5.11.37.293.1031.3163.7390043.7740379.220836773.236564659.352842173

Input number is (2011^64+1150^64)/19042614590745118428708764176581757441 (175 digits)
Using B1=51000000-1000000000, B2=205702371522480, polynomial x^1
Step 1 took 343358ms
********** Factor found in step 1: 262428378691151920451118182145223566271724639692992641
Found probable prime factor of 54 digits: 262428378691151920451118182145223566271724639692992641
Composite cofactor ((2011^64+1150^64)/19042614590745118428708764176581757441)/262428378691151920451118182145223566271724639692992641 has 121 digits
Report your potential champion to Paul Zimmermann 
(see http://www.loria.fr/~zimmerma/records/Pminus1.html)



January 11, 2011 (Kurt Beschorner, GMP-ECM, B1=11e6, sigma=4055434517)

41^128+40^128: 14415041380564586302619439644134010790913.



January 7, 2011

2010 completely unfactored numbers of shape 2011^64+b^64 are collected in http://www.AlfredReich.com/GF.2011.64.txt.

40 completely unfactored numbers of shape 41^128+b^128 are collected in http://www.AlfredReich.com/GF.41.128.txt.
40 completely unfactored numbers of shape 41^256+b^256 are collected in http://www.AlfredReich.com/GF.41.256.txt.
40 completely unfactored numbers of shape 41^512+b^512 are collected in http://www.AlfredReich.com/GF.41.512.txt.
40 completely unfactored numbers of shape 41^1024+b^128 are collected in http://www.AlfredReich.com/GF.41.1024.txt.

Contributions are very welcome. Any factor, any size.



January 6, 2011

40 factorizations of numbers of shape 41^64+b^64 are summarized in http://AlfredReich.com/GF.41.64.txt.



January 5, 2011 (Msieve - QS)

(194L^2*41)^41-1: c116 = p47 * p69, where
                  c116 = 14089578077248626892538296849311850343582170391961042897771655611847090411180410624646802935810345878870788095819901,
                   p47 = 83520685764890265759258749938481016547324302343 and
                   p69 = 168695670398476146705592244277109397986816460098886249291325088124507.



January 1, 2011 (P-1)

10^36150L+1: 74947808045149231201.
10^36590M+1: 14074864070290137581.
10^37330L+1: 27335775958499401.
10^42770L+1: 11460585387161.
10^42910L+1: 1943672619369728559761.
10^49790L+1: 1171792107852341.

10^10545+1: 331429772696710693921.
10^11125+1: 2060132682052434251.



January 1, 2011

528 factorizations of numbers of shape 2010^32+b^32 are summarized in http://AlfredReich.com/GF.2010.32.txt.


Alfred Reich