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streamVolunteer moderator
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The Factorial Prime Search is the last project from factorial group. This group consist of three projects very close related to each other:
- Factorial, or n! - known to you from school years, a product of all numbers <= n;
- Primorial, or n# - a product of all prime numbers <= n. A good detailed description can be found in this post;
- Compositorial - product of all non-prime (composite) numbers <= n. Compositorial has no own mathematical character and can be written as n!/n# .
In the factorial prime search, we'll search for primes having form of n! +/- 1.
Search will be started from n=310000. All candidates below were tested here on PrpNet and double-checked later. Current limit of this search is n=2000000, it's many years of work.
The largest known factorial prime is 632760!-1, found by independent searcher. It's expected that range between 310000 and 632760 has already been tested and should have no new primes. Anyway, we're double-checking this range to be sure that there were no hardware of software errors and no primes were missed.
For additional technical information, please also check compositorials thread because both projects are using same software and size of candidates is very close.
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Excellent. We can all get a new badge. And if we are extremely lucky, all the independent searchers were sloppy and uncoordinated enough that they missed a prime. Unlikely, perhaps, but it brings a little hope.
Thank you Stream (and others) for making this happen!
/JeppeSN |
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Here is the relevant old glossary entry on T5k: factorial prime
And here is the list of all "big" factorial primes currently known, both by PrimeGrid PRPNet and by everyone else, also on T5k: Top Twenty: Factorial primes
Finally, our own status page for this subproject: /stats_fps.php
/JeppeSN |
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What about CPU cache requirements? |
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What about CPU cache requirements?
I can quote something Stream said on Discord:
It'll start from FFT 2x288K, but at n=400K (which we should reach quickly enough) FFT will be 2x360K. It means *at least* 4.6Mb and 5.7Mb cache per task, correspondingly. So multithreading is necessary for most setups.
/JeppeSN |
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Are the remaining tasks (currently 28K) from the main page all that is left? Are there more after that? |
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from stream's first post: Search will be started from n=310000. All candidates below were tested here on PrpNet and double-checked later. Current limit of this search is n=2000000, it's many years of work.
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Honza  Volunteer moderator
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Leading edge reached 500k.
AVX-512 FFT length 2x448K
Candidate size around 2.6M
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Honza Volunteer moderator
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Leading edge reached 600k.
AVX-512 FFT length 2x576K
Candidate size around 3.2M
We are closing on 632760
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 robish Volunteer moderator
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Leading edge reached 600k.
AVX-512 FFT length 2x576K
Candidate size around 3.2M
We are closing on 632760
👍
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My lucky number 10590941048576+1 |
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Leading edge now reached n=632821 so now is a good opportunty to find a new and bigger Factorial Prime!
Good hunting every one!!
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Honza Volunteer moderator
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Also recently...
AVX-512 FFT length 2x588K
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With Snake Day challenge coming up, factorial will get a big push forward.
As already mentioned by others above, any prime found now will be a world record for factorial primes. (We cannot know if "independent searchers" have already crunched in the current region, but if they have, then they failed to locate any prime.)
/JeppeSN |
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