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Old 2010-10-16, 13:55   #19
lorgix
 
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Sep 2010
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Quote:
Originally Posted by TheJudger View Post
Hi,



I think so, some of "my" P-1 factors, sorted by factor size:

M49915309 has a factor: 2085962683046854861393 (70.82 Bits; k = 20895019231944 = 2 * 2 * 2 * 3 * 11 * 13 * 37 * 227 * 347 * 2089)
M50739071 has a factor: 10474816683392115991831 (73.14 Bits; k = 103222393285365 = 3 * 3 * 5 * 19 * 181 * 227 * 769 * 3821)
M51027377 has a factor: 77850684812475802805663 (76.04 Bits; k = 762832516479103 = 7 * 17 * 139 * 191 * 239 * 257 * 3931)
M51679921 has a factor: 451068222670482355938121 (78.57 Bits; k = 4364056812997860 = 2 * 2 * 3 * 5 * 11 * 307 * 953 * 2957 * 7643)
M53196851 has a factor: 129375114189794147350126111 (86.74 Bits; k = 1216003501690298805 = 3 * 5 * 11 * 17 * 71 * 79 * 2113 * 3571 * 10243)
M51007903 has a factor: 416373044176966390884620641 (88.42 Bits; k = 4081456202747311440 = 2 * 2 * 2 * 2 * 3 * 3 * 3 * 5 * 13 * 59 * 89 * 563 * 4441 * 11071)
M51094921 has a factor: 620135167283167713317314151 (89.00 Bits; k = 6068461944418778075 = 5 * 5 * 271 * 2851 * 3371 * 8429 * 11057)
M51139447 has a factor: 1873562419055481575542379948831 (100.56 Bits; k = 18318172457510946251945 = 5 * 7 * 19 * 23 * 73 * 359 * 18457 * 35597 * 69557)

Oliver
Quote:
Originally Posted by alpertron View Post
But notice the latest factors my computer found using ECM:

M400087 has a factor: 286218557414155282359049 (k = 2 ^ 2 x 3 x 41737 x 714185251333)
M400277 has a factor: 2081610233687632912124807 (k = 11 x 107 x 2209186189633807)

These factors could not have been discovered using P-1.

Yes, both extremes exist.

But I'm curious about how common cases like these are.

A 3D (exponent size, number of factors of k, sizes of factors of k) graph or a distribution table would be extremely nice. But I doubt that's at hand.

Any thought or info/ideas?
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