Double Factors

[Gordon]

I've run a few ranges up in the hundreds of millions and on three occasions have had mfaktc return two factors for the same exponent.

For the first time today I have had the same in the "normal" work-space, a 40m double check in fact.

UID: nitro/GTX-970, M40553413 has a factor: 4628777451145663818113 [TF:71:72:mfaktc 0.21 barrett76_mul32_gs]
UID: nitro/GTX-970, M40553413 has a factor: 2957800359711131127671 [TF:71:72:mfaktc 0.21 barrett76_mul32_gs]
UID: nitro/GTX-970, found 2 factors for M40553413 from 2^71 to 2^72 [mfaktc 0.21 barrett76_mul32_gs]

How often should we expect this to arise? In other words is this a rare event?

For interest here are the others

UID: nitro/NVidia, M374011241 has a factor: 255127733487162275449 [TF:66:69:mfaktc 0.20 barrett76_mul32_gs]
UID: nitro/NVidia, M374011241 has a factor: 374875803406924157593 [TF:66:69:mfaktc 0.20 barrett76_mul32_gs]
UID: nitro/NVidia, found 2 factors for M374011241 from 2^66 to 2^69 [mfaktc 0.20 barrett76_mul32_gs]

UID: nitro/NVidia, M800074609 has a factor: 278430345631804693927 [TF:66:68:mfaktc 0.20 barrett76_mul32_gs]
UID: nitro/NVidia, M800074609 has a factor: 201002749157149138999 [TF:66:68:mfaktc 0.20 barrett76_mul32_gs]
UID: nitro/NVidia, found 2 factors for M800074609 from 2^66 to 2^68 [mfaktc 0.20 barrett76_mul32_gs]

UID: nitro/NVidia, M800079893 has a factor: 87320074164777027913 [TF:66:68:mfaktc 0.20 barrett76_mul32_gs]
UID: nitro/NVidia, M800079893 has a factor: 107522046708157973279 [TF:66:68:mfaktc 0.20 barrett76_mul32_gs]
UID: nitro/NVidia, found 2 factors for M800079893 from 2^66 to 2^68 [mfaktc 0.20 barrett76_mul32_gs]

[VictordeHolland]

It depends on your settings in mfaktc/mfakto config:

# possible values for StopAfterFactor:
# 0: Do not stop the current assignment after a factor was found.
# 1: When a factor was found for the current assignment stop after the
#    current bitlevel. This makes only sense when Stages is enabled.
# 2: When a factor was found for the current assignment stop after the
#    current class.
#
# Default: StopAfterFactor=2

If you choose the default (StopAfterFactor=2), you will find them extremely rarely. Option 1 will occasionally find 2 (or more) factors in a bitlevel. With option 0, your GPU will do all the assigned bitlevels even if a factor is found (and thus has a chance to find another factor at a higher bitlevel).

Note: for the progress of finding Mersenne Primes, finding a single factor rules that exponent out of being prime.
It depends on your view if you want to complete the current bitlevel after a factor is found. I 'understand' a trial factoring assignment as: trial factor from x bits until a factor is found (success) or y bits (assignment complete). Some people complete the current bitlevel for clearness/tidiness/clarity (or just want to have some fun with finding multiple factors).

[xilman]

Originally Posted by VictordeHolland

ISome people complete the current bitlevel for clearness/tidiness/clarity (or just want to have some fun with finding multiple factors).

And some people have fun finding factors rather than finding Mersenne primes. I've been in this class for a very long time now.

It takes all sorts.