User TJAOI

[axn]

Originally Posted by TheMawn

It's analogous to me saying that the results are more expensive to get.

Fun exercise: At what error rate is it worthwhile to redo factoring 64-68 range instead of freshly doing 74-75 on the same exponent?

[petrw1]

Manual testing 77972753 F 2015-01-25 02:26 0.0 449727144997821167993 0.4659 
Manual testing 77783977 F 2015-01-24 18:26 0.0 90277075440550289359 0.0559 
Manual testing 77719069 F 2015-01-24 14:27 0.0 1043300478855676685249 1.2640 
Manual testing 77711563 F 2015-01-24 14:27 0.0 819036389770912845839 0.7270 
Manual testing 77705449 F 2015-01-24 14:27 0.0 290868301272790451633 0.3766 
Manual testing 77677547 F 2015-01-24 10:26 0.0 832564635208119196727 0.7637 
Manual testing 77619533 F 2015-01-24 10:26 0.0 1027401748819195733953 1.2315 
Manual testing 77551121 F 2015-01-24 06:27 0.0 346663356744036424591 0.1789 
Manual testing 77370851 F 2015-01-23 22:27 0.0 404115972658736858983 0.3503 
Manual testing 77307031 F 2015-01-23 22:27 0.0 438083349942146687417 0.4406 
Manual testing 77011177 F 2015-01-23 10:27 0.0 305268169799265418919 0.0378 
Manual testing 72675403 F 2015-01-22 22:27 0.0 525252945259548579551 0.6840 
Manual testing 72605201 F 2015-01-22 18:27 0.0 500990223783061289983 0.6285 
Manual testing 72562397 F 2015-01-22 18:27 0.0 87831182112341748793 0.0518 
Manual testing 72523147 F 2015-01-22 18:27 0.0 335176031292832929289 0.1512 
Manual testing 72506251 F 2015-01-22 18:27 0.0 336037822780058053313 0.1543 
Manual testing 72401041 F 2015-01-22 14:27 0.0 218291136715616382799 0.2332 
Manual testing 72382501 F 2015-01-22 14:27 0.0 342944142087508898161 0.1788 
Manual testing 72363173 F 2015-01-22 14:27 0.0 544002637626766728503 0.7288 
Manual testing 72349657 F 2015-01-22 14:27 0.0 315890959036043643191 0.0810 
Manual testing 72337151 F 2015-01-22 14:27 0.0 34504309201726567649 0.0467 
Manual testing 72237229 F 2015-01-22 10:27 0.0 364475248423316556359 0.2519 
Manual testing 72180077 F 2015-01-22 10:27 0.0 210713469140678257513 0.212

[Miszka]

Sannerud.com didn't go TF only according to me he sent prepared files. Adding to manual testing results Checksums e.g. you should prevent this.

[S485122]

Originally Posted by Miszka

Sannerud.com didn't go TF only according to me he sent prepared files. Adding to manual testing results Checksums e.g. you should prevent this.

As George said only one laptop of Sannrud failed to find factors at the expected rate, his other machines found factors "normally". Therefore the conclusion is not that he cheated but that one of his machines, a laptop, had (has) a hardware problem. The prime95 (mprime) code has no way to check for hardware errors in trial factoring, it has in LL tests.

Jacob

[bloodIce]

Originally Posted by TheMawn

The goal of this project is to find the next Mersenne Prime. Trial factoring eliminates potential candidates. This much is clear.

The smart question is: "How much TF do we do?" but that is easy to answer. Using easy numbers as an example: If it takes 100 GHz-Days to do an LL test, finding a factor will save 200 GHz-Days. If we have a 1 in 100 chance of finding a factor, then it is reasonable for us to invest 2 GHz-Days into that TF because on average, after 100 candidates, we will have eliminated 200 GHz-Days worth of LL and it cost us 200 GHz-Days of TF.

Here I agree almost completely. The arguments put by LaurV in that respect are valid though: how your hardware performs the best in a range and what your preferences are. However, yes from GIMPS point of view, your calculation makes perfect sense.

Originally Posted by TheMawn

Now, why do we re-do the TF? Well, the goal of this project is to find the next Mersenne Prime, and re-doing the Trial Factoring eliminates potential candidates.

The smart question is: "How much TF do we do?" but that is not so easy to answer. It still takes 100 GHz-Days to do the LL test and finding the factor still saves 200 GHz-Days, but what is the chance of finding a factor now? This is hard to tell. If it WAS 1 in 100 with a "fresh" run, it has to be less than 1 in 100 now.

For example, if I attempted 10,000 TF runs and found 75 factors (as opposed to the expected 100) then it is reasonable to suggest that I might have missed 25. If you're going to repeat my work, suddenly your odds of finding a factor are 1 in 400. Which means that it is now only reasonable for you to invest 0.5 GHz-Days into that TF, because on average, after 400 candidates, we will have eliminated 200 GHz-Days worth of LL at a cost of 200 GHz-Days of TF.

OK, this holds, but my question is: How do you know the error rate a priori? How do you know it is 1 to 4, 1 to 2 or 1 to 10?
On non-compromised machine the error rate is 1 to trillion or less, but how much will be on a faulty hardware? How faulty? How do you know?

And second question: Why do you think that everyone should do something that is the most optimal? Where is the fun factor. At the end GIMPS is a voluntary project, not a military aim. Why not let me take the risk of a TF below the expected probability for a factor? That is close to take 100 random TF assignments form PrimeNet and to believe that at least one factor will appear. Obviously not guaranteed. So, should you do it at all?

[Chuck]

Originally Posted by Chuck

Finally finished with the 75M and 76M ranges. Towards the end it seemed like the job would never end. I found forty factors.

75060761 75259127 75287159 75318389 75457573 75661711 75675931 75876391 75908453 75956273 75979559 75992603 75997279 76012159 76057207 76099057 76100447 76132493 76178237 76343623 76349659 76370207 76411163 76452569 76458259 76476677 76493933 76529683 76600393 76608913 76682797 76686217 76692937 76712039 76713761 76718441 76733357 76811629 76844221 76943201

I checked 1,236 numbers total.

Why did I find so many factors? 40 found out of 1,236 tested is nearly 1 in 31. Shouldn't this have been nearer 1 in 75 or 76?

[Uncwilly]

Originally Posted by Chuck

Why did I find so many factors? 40 found out of 1,236 tested is nearly 1 in 31. Shouldn't this have been nearer 1 in 75 or 76?

Use James's tool to calculate the probability of finding a factor for a single assignment, then multiply that by the number of your assignments. See what you get.

[Chuck]

Oh I forgot it's not the exponent but the bit level that determines the probability; still, these were in the range of 67 to 70 bits and 1 out of 31 is a lot more than 1 out of 67.

[LaurV]

Many of them were multiple bits (like 65 to 67, and I even have seen one like 63 to 68? So if you split them, you had much more than 1200 assignments).

[Chuck]

Originally Posted by LaurV

Many of them were multiple bits (like 65 to 67, and I even have seen one like 63 to 68? So if you split them, you had much more than 1200 assignments).

You're right, that makes sense of it.

[kladner]

Factors to date. 122 left to do.

M79483499 has a factor: 262360609558645869361 [TF:67:68*:mfaktc 0.20 barrett76_mul32_gs]
M79466503 has a factor: 158171873142735543391 [TF:67:68*:mfaktc 0.20 barrett76_mul32_gs]
M79406497 has a factor: 142926079712600712041 [TF:66:67*:mfaktc 0.20 barrett76_mul32_gs]

M79359781 has a factor: 86018707765317281777 [TF:66:67*:mfaktc 0.20 barrett76_mul32_gs]
M79329049 has a factor: 436594536103628352239 [TF:68:69*:mfaktc 0.20 barrett76_mul32_gs]
M79227053 has a factor: 465022048023243077879 [TF:68:69*:mfaktc 0.20 barrett76_mul32_gs]
M79004249 has a factor: 234687434795636918167 [TF:67:68*:mfaktc 0.20 barrett76_mul32_gs]
M79033063 has a factor: 463838510863801116457 [TF:68:69*:mfaktc 0.20 barrett76_mul32_gs]

M79388209 has a factor: 635545254030291494921 [TF:69:70*:mfaktc 0.20 barrett76_mul32_gs]
M79387769 has a factor: 232488207444013028009 [TF:67:68*:mfaktc 0.20 barrett76_mul32_gs]
M79383181 has a factor: 278890815675960387673 [TF:67:68*:mfaktc 0.20 barrett76_mul32_gs]
M79373999 has a factor: 42176261588351110289 [TF:65:67*:mfaktc 0.20 barrett76_mul32_gs]
M79362671 has a factor: 396626201607035962649 [TF:68:69*:mfaktc 0.20 barrett76_mul32_gs]