fond of a factor? Urn yourself to become inane

[masser]

M14039173 has a factor: 4281610697981019482542271 (P-1, B1=550000, B2=550000, e=12, n=800K CUDAPm1 v0.22)

P-1 = 4 281610 697981 019482 542270 = 2 × 5 × 131 × 193 × 2243 × 20147 × 26693 × 14 039173

Another factor missed by late-2001 P-1 result.

[petrw1]

Originally Posted by masser

M14039173 has a factor: 4281610697981019482542271 (P-1, B1=550000, B2=550000, e=12, n=800K CUDAPm1 v0.22)

P-1 = 4 281610 697981 019482 542270 = 2 × 5 × 131 × 193 × 2243 × 20147 × 26693 × 14 039173

Another factor missed by late-2001 P-1 result.

I believe this was found by the Brent Suyama extension. The last factor of K is very high

[James Heinrich]

Originally Posted by masser

P-1 = 4 281610 697981 019482 542270 = 2 × 5 × 131 × 193 × 2243 × 20147 × 26693 × 14 039173

Originally Posted by petrw1

I believe this was found by the Brent Suyama extension. The last factor of K is very high

No, the last factor as written by masser is the exponent, as expected.
Remembering that Mersenne factors occur in the form of 2 * exponent * k + 1, in this case:
4281610697981019482542271 = 2 * 14039173 * (5 × 131 × 193 × 2243 × 20147 × 26693) + 1
(masser expressed this with 1 removed from both sides)

The factor should have been found in stage1 of the original P-1 run in 2001, another victim of buggy P-1 implementation in early Prime95.

[petrw1]

Originally Posted by James Heinrich

No, the last factor as written .....

[petrw1]

Originally Posted by James Heinrich

The factor should have been found in stage1 of the original P-1 run in 2001, another victim of buggy P-1 implementation in early Prime95.

Are there enough errors that its worth redoing all early P1s from a certain time frame? Wouldn't take nearly as long now

[James Heinrich]

Originally Posted by petrw1

Are there enough errors that its worth redoing all early P1s from a certain time frame? Wouldn't take nearly as long now

Probably. A handful of us are already redoing badly-done P-1 in the 10M-20M range and found a bunch. I can't speak for anyone else but I'm working through all the poor-probability (mostly stage1-only) P-1 up to 20M, and finding a fair number of factors for relatively little effort. Some of these may have been missed-factors, others just because previous bounds were too low, I haven't investigated. Possibly at some point it would be worth compiling a list of exponents with no known factors that had a NF-PM1 reported during the probably time period (prior to 2003?) and having a go at them. A project for next year, perhaps.

[petrw1]

68613220865556854534588910185633642635647672703702073263
Composite factor found for 43028351 with P-1.
Has two 7-digit palindromes within it:

The corresponding Prime Factors
84906808619428164689743
808100339433284836173218656436641
The smaller has a 5-digit palindrome within it.
The middle 3 digits of which are the beginning of the larger factor.

[storm5510]

Originally Posted by James Heinrich

Probably. A handful of us are already redoing badly-done P-1 in the 10M-20M range and found a bunch. I can't speak for anyone else but I'm working through all the poor-probability (mostly stage1-only) P-1 up to 20M...

I used to run some of these. I would take an entire list of 500 and save it to a file, and run them in order in smaller groups. I used Prime95, avoiding the extra step in getting AID's then moving them to something else. I never felt Prime95's bounds were high enough, and I was never sure how many it would allow me reserve in each group without cutting my list off somewhere at the bottom. The most I ever tried was 50.

What I ran then were all between 7e6 and 8e6. I just generated another list. What I see now starts just below 37e5 and ascends rapidly, so some new ones have been added to the lower end.

[James Heinrich]

M12469069 has a 209.296-bit (64-digit) composite (P30+P34) factor: 1010407523290974831570787304355977539700408276934619634505308431 (P-1,B1=635000,B2=27600000,E=12)

But I can't take credit for that. It was actually found in 2001 by "chbarr2". However, for a short while in those early days, PrimeNet would accept composite factor results but only record the first/smallest prime factor. I discovered this by accident, so I went through all the result logs looking for where a composite factor was reported but not all prime component factors were recorded. I found about a dozen, and they have all been "rediscovered" and recorded now, and back-dated to their original date of discovery. Also note that in those early days, PrimeNet kept no record of factor discovery method, all factors were just lumped together with TF results.

[Uncwilly]

George just found a biggy:
100817777 has a factor 7594873610247018123015770141312996569
37 digits 122.5 bits

Ken found a big one too:
101273659 has a factor 375324496211112358228921438201039041097
39 digits 128.1 bits

[James Heinrich]

And George's wasn't even with Prime95 (but rather gpuowl).