Missed small factors

[GP2]

I have completed them to 57 bits, no factors.

Note, 14.64-14.66 of course means 14.64... and 14.65...

Go ahead, and let us know if you find anything.

[PageFault]

FYI,

I had a machine which produced only bad LL results. I tested whether it might be useful for tf work, feeding it a worktodo made up of all my factoring finds. This was successful, all factors found were identical. Factors were found previously on different hardware and architecture using a much older version of client ... havent done factoring in a few years.

[nfortino]

All 488 exponents have been trial factored to 58 bits, no factors found.
I have attached a file containing the results, mainly to confirm we are doing the same exponents.

[GP2]

Yes, they're the same exponents... straight out of the "nofactor" file.

[GP2]

I'm going to do these 488 exponents to 59 bits.

I'm increasingly convinced though, that the lower than expected number of factors in this range is just statistical noise.

Edit: all done, no factors found to 59 bits.

[error404]

dswanson,

This is another missed small factor, 17 digits or
57 bits in length. The reported TF depth:
Factor=4312549,61

[Sat Apr 17 16:37:12 2004]
P-1 found a factor in stage #2, B1=2048, B2=204800.
UID: k5gj/2, M4312549 has a factor: 38488046970367391

Tom

[mianfei]

A question that has always interested me is whether any small factors were missed in the pre-computer era for Mersenne numbers M263 and larger??

Looking at a modern factor table and with the knowledge I have as to what numbers could be partially factored before 1952, it seems clear to me that, even if we exclude cases where 2p+1 divides 2^p-1 and do not go beyond p = 509, there exist quite small (below 75,000) factors of 2^p-1 for p = 263, 283, 317, 337, 367, 397 (as many as four <75,000), 461, 463, 487 and 499.

I am very curious as to see when these small factors were found.

[markr]

Just for fun, on and off over the last few months I have done some more hunting for missed factors in the 6.0M and 7.0M areas. My early stages were a bit of a patchwork, but I've filled in the gaps I'd left and it's time to report. I still reckon there are more factors out there - we just have to find them!

In 6.0M, the LMHers and GP2 checked 5.977M-6002281 to 2^62; I went to 6.03M, but only to 2^61.

In 7.0M, dswanson had checked 7.019M-7.055M to 2^59. I extended the search to 7.055M-7.06M to 2^59, and 7.019M-ongoing to 2^60.

These are the factors found so far; I submitted them gradually, as I found them (not in this order!) except for the most recent couple as the manual pages aren't working. All these exponents were in nofactor at 62 or 63 bits.

exponent,factorbits,factor
6009539,59,406714140975740687
6013123,56,44181679325739161
6016093,58,212097137467163833
6017399,57,134579629908406297
6017477,60,593050922868025703
6017741,61,2205549478919843993
6017777,59,495633521948668463
6018037,57,105416832029893129
6018191,60,849841748091574657
6018197,60,1150871070238181657
6018577,57,120037098124359673
6020087,56,36743171278649767
6020449,56,43976684361205639
6021073,61,1735918705958765033
6023701,56,61752215544471631
7020529,60,597000447877349071
7033163,60,672873669487836367
7034761,60,1076436975701332913
7056611,56,47304117008665919
7056943,56,39371367276363127
7057331,53,8301399750516527
7057333,53,7650834987111599

[markr]

7.019M - 7.06M is now complete to 2^60, with three more factors found:

exponent,factorbits,factor
7045039,60,680045266294721737
7051711,60,871423793297241281
7057103,60,1006060557272490673

The last one has been sent in but is not in factors.cmp yet.

That's enough for me until I spend some time thinking about where to look next. It's been a good use for a very slow computer - 25 factors in all.