Unlucky in l̶o̶v̶e̶ factoring? - Page 3

Andrew Usher · 2023-06-27, 23:57

Given the old and new bounds there, the chance of no factor in 20 tries is about half. Not very unlucky, yet. (Take the difference of the two in the mersenne.ca calculator - if the old used Brent-Suyama, approximate its effect by increasing B2 by 10%).

I might as well comment on the last topic though the data used for it are entirely obsolete. The server (then and now) is supposed to mark an exponent 'available for P-1' (and not for TF) when it reaches 1 bit _below_ the standard TF level. This derives from the old practice of CPU factoring running P-1 before the last bit of TF. But if there ever was, there's no mechanism now that assigns that last bit after P-1 is done, so that 1-bit margin really shouldn't exist anymore.

Magellan3s · 2023-06-28, 01:15

I average about 10~ish factors for every 1,000 I attempt when trial factoring to 75 bits.

Andrew Usher · 2023-06-28, 23:20

That's not very well-defined. As you should know the probability should be the reciprocal of bit-level - accuracy requires using the average of the low and high ends, and correcting for multiple factors, so 1.32% to the nearest 0.01% for 74-75. 10 per 1000 (1%) might be a crude 'eyeball estimate', but it's not your actual odds - it is impossible to be persistently 'unlucky' at this, so if you've made e.g. 20,000 attempts and had exactly 200 factors, your gear probably has an issue (>4 sigma below expected).

Uncwilly · 2023-06-28, 23:36

Quote:

Originally Posted by Andrew Usher

As you should know the probability should be the reciprocal of bit-level

That had been a working estimate. The accuracy of that estimate appears to break down somewhere in the 75 bit range. It does approach 1/100. This is based upon large amounts of data across many users.

Andrew Usher · 2023-06-29, 12:57

That relationship is extremely well-grounded mathematically, depending essentially on the prime number theorem. It would require extraordinary data to overturn that belief, such as double-checking a large range with different software and finding nothing. And it certainly should not suddenly change at any given bit level, though if caused by random errors it may appear to - that is the most likely explanation for any persistent shortfall.

charybdis · 2023-06-29, 16:58

Quote:

Originally Posted by Uncwilly

That had been a working estimate. The accuracy of that estimate appears to break down somewhere in the 75 bit range. It does approach 1/100. This is based upon large amounts of data across many users.

Do you genuinely see a much smaller number of 75-bit factors compared to, say, 72-bit factors? If so, this would be indicative of a major software bug.

Uncwilly · 2023-06-29, 17:45

Chalsall has seen it overall with the various folks using GPU72. IIRC.
https://www.mersenneforum.org/showpo...&postcount=465

charybdis · 2023-06-29, 19:56

Quote:

Originally Posted by Uncwilly

Chalsall has seen it overall with the various folks using GPU72. IIRC.
https://www.mersenneforum.org/showpo...&postcount=465

Don't see any actual data there, or anything saying the rate of factors dropped.
(Disregard the rest of my previous post, of course if TF was missing factors then P-1 would find them)

Uncwilly · 2023-06-29, 20:04

Chris has mentioned it other times, this is the only one that I can find (quickly). It is not a sudden drop. But starting around 75 or so, the 1/x ratio begins to fade to be closer to 1/100 by around 79. Those that are great data mavens might be able to produce the data to back this up.

chalsall · 2023-06-29, 21:38

Quote:

Originally Posted by charybdis

Don't see any actual data there, or anything saying the rate of factors dropped. (Disregard the rest of my previous post, of course if TF was missing factors then P-1 would find them)

I do *love* the empirical. Corrects all, when appropriate!

This report is *very* expensive, so please don't click it unless you can really use the data.

But... this is the query against the GPU72 database with regards to factors found *through GPU72*. As in, this is a sub-set of what Primenet knows about.

I actually haven't looked at this report myself for years. And it doesn't cover ranges above 86M; how time flies when you're having fun! 8^)

What *I* see in the data is indeed prior P-1 work has the expected impact on TF success heuristics.

So the Theorists win again!!! 9^)

chalsall · 2023-06-29, 22:04

That is *really* interesting empirical data.

And, unfortunately, it was written so long ago that it doesn't cover contemporary ranges. We were only going to 75 back then.

I don't have time to expand this query. Perhaps over the weekend.

Can anyone on the Primenet side of the house build a simple query and expose the data as a CSV et al for those who "Don't Get Out Much"^TM?

2023-06-29, 17:45	#29
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 10101100111011₂ Posts	Chalsall has seen it overall with the various folks using GPU72. IIRC. https://www.mersenneforum.org/showpo...&postcount=465 Last fiddled with by Uncwilly on 2023-06-29 at 17:55

2023-06-29, 22:04	#33
chalsall If I May "Chris Halsall" Sep 2002 Barbados 11374₁₀ Posts	Hmmm... That is really interesting empirical data. And, unfortunately, it was written so long ago that it doesn't cover contemporary ranges. We were only going to 75 back then. I don't have time to expand this query. Perhaps over the weekend. Can anyone on the Primenet side of the house build a simple query and expose the data as a CSV et al for those who "Don't Get Out Much"^TM?

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2023-06-27, 23:57	#23
Andrew Usher Dec 2022 3×13² Posts	Given the old and new bounds there, the chance of no factor in 20 tries is about half. Not very unlucky, yet. (Take the difference of the two in the mersenne.ca calculator - if the old used Brent-Suyama, approximate its effect by increasing B2 by 10%). I might as well comment on the last topic though the data used for it are entirely obsolete. The server (then and now) is supposed to mark an exponent 'available for P-1' (and not for TF) when it reaches 1 bit _below_ the standard TF level. This derives from the old practice of CPU factoring running P-1 before the last bit of TF. But if there ever was, there's no mechanism now that assigns that last bit after P-1 is done, so that 1-bit margin really shouldn't exist anymore.

2023-06-28, 01:15	#24
Magellan3s Mar 2022 Earth 7E₁₆ Posts	I average about 10~ish factors for every 1,000 I attempt when trial factoring to 75 bits.

2023-06-28, 23:20	#25
Andrew Usher Dec 2022 3×13² Posts	That's not very well-defined. As you should know the probability should be the reciprocal of bit-level - accuracy requires using the average of the low and high ends, and correcting for multiple factors, so 1.32% to the nearest 0.01% for 74-75. 10 per 1000 (1%) might be a crude 'eyeball estimate', but it's not your actual odds - it is impossible to be persistently 'unlucky' at this, so if you've made e.g. 20,000 attempts and had exactly 200 factors, your gear probably has an issue (>4 sigma below expected).

2023-06-29, 12:57	#27
Andrew Usher Dec 2022 773₈ Posts	That relationship is extremely well-grounded mathematically, depending essentially on the prime number theorem. It would require extraordinary data to overturn that belief, such as double-checking a large range with different software and finding nothing. And it certainly should not suddenly change at any given bit level, though if caused by random errors it may appear to - that is the most likely explanation for any persistent shortfall.

2023-06-29, 20:04	#31
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 3·7·17·31 Posts	Chris has mentioned it other times, this is the only one that I can find (quickly). It is not a sudden drop. But starting around 75 or so, the 1/x ratio begins to fade to be closer to 1/100 by around 79. Those that are great data mavens might be able to produce the data to back this up.