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Old 2019-07-02, 05:11   #199
SethTro
 
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I read about 80% of this thread and tried to follow all the math based suggestions.

@Preda's posts, especially 58 and 122, are great.
https://www.mersenneforum.org/showpo...7&postcount=58
https://www.mersenneforum.org/showpo...&postcount=122

I had the same ideas after reading the initial idea by Robert Gerbicz
https://www.mersenneforum.org/showpo...7&postcount=30

I have another adapting that I believe can solve one of the listed drawbacks



We can also adapt a solution used by bitcoin mining pools (where they similarly miners to have success mining (e.g. "see a factor") only rarely).

Instead of giving binary all or nothing credit (and hoping it averages over a long period of timing) give credit proportional to the smallness of min(x) or min(bitrev(x). Now each result earns between 1/32 and ~4 credit on each submission. This function is much less noisy than the binary 0/1 reward so even when turning in a bunch of no factor found results you would still expect to receive, on average, full credit (I can write a simulator if people want graphs).

Now hypothetical cheater would get credit exactly equal to the work done on average. It doesn't stop them lying about the work done (that can maybe be detected later with static user analysis) but they're reward is now verifiable linked to the work they performed
I wrote up a 80% of the code needed for this
https://github.com/sethtroisi/mfaktc/tree/master

mod_simple_96_and_check_big_factor96 doesn't calculate the modulo so it uses a slightly different Proof-of-work function (instead producing very large modulos instead of small)
https://github.com/sethtroisi/mfaktc...helper.cu#L244

The end result is on TF-NF results you get a little extra line like this
Code:
M59068201 proof_k(17257705361971287559): 30 bits [TF:60:64:mfaktc 0.21 75bit_mul32_gs]
M59068201 proof_k(1759939290551364353): 31 bits [TF:60:64:mfaktc 0.21 75bit_mul32_gs]
M59068201 proof_k(1297657372566442343): 31 bits [TF:60:64:mfaktc 0.21 75bit_mul32_gs]
M59068201 proof_k(8940824503190951977): 29 bits [TF:60:64:mfaktc 0.21 75bit_mul32_gs]
[Mon Jul  1 21:59:54 2019]
no factor for M59068201 from 2^60 to 2^64 [mfaktc 0.21 75bit_mul32_gs]
You can then verify that pow(2, 59068201, 8940824503190951977) = 422536362 which is 29 bits meaning ~34 leading zeros bits. so it takes around ~1e11 test to find this (which is handily just about 2^64 / 59068201)
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Old 2020-01-09, 01:29   #200
SethTro
 
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What's the appropriate way to report probable false results?

M14951 has a P-1 result with B2=9,887,122,214,540,712 which took an estimated 186,161 GHzDays (I guess this isn't impossible, but seems unlikely given the user doesn't appear on any of the top producer lists are regularly submit factors)
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Old 2020-01-09, 02:48   #201
axn
 
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What's the appropriate way to report probable false results?

M14951 has a P-1 result with B2=9,887,122,214,540,712 which took an estimated 186,161 GHzDays (I guess this isn't impossible, but seems unlikely given the user doesn't appear on any of the top producer lists are regularly submit factors)
This is a perfectly doable range if you use P95 for stage1 and GMP-ECM for stage 2. The 186k GHzdays is granted based on the assumption that stage 2 was done with P95.
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Old 2020-01-09, 04:24   #202
SethTro
 
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This is a perfectly doable range if you use P95 for stage1 and GMP-ECM for stage 2. The 186k GHzdays is granted based on the assumption that stage 2 was done with P95.
It sticks out quite a bit on the factoring limit page. with B2=9e15 it's the 2nd largest B2 and 2-3 orders of magnitude larger than the B2 of nearby exponents (M10061 had B2=1e14, M16411 had B2=5e12)

https://www.mersenne.org/report_fact...99&tftobits=72
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Old 2020-01-09, 06:38   #203
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It sticks out quite a bit on the factoring limit page. with B2=9e15 it's the 2nd largest B2 and 2-3 orders of magnitude larger than the B2 of nearby exponents (M10061 had B2=1e14, M16411 had B2=5e12)

https://www.mersenne.org/report_fact...99&tftobits=72
From the ratio of B2/B1, it looks like most of them were done with P95 for both stages. Couple of them, 2719 and 14951 sticks out.

Like I said, this is perfectly normal _if_ GMP ECM was used for stage 2. Unless you have some reason to believe that these are specifically fraudulent (apart from the large B2), I suggest that you make peace with it.
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