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Message boards : Proth Prime Search : n and k ranges for PPS SV?

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Bur
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Message 143598 - Posted: 23 Sep 2020 | 17:35:35 UTC

Which k and n ranges does the sieve cover? And how many candidates are still in the sieve?
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Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^8-1979 & 1281979 + 4 (cousin prime)

JeppeSN

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Message 143600 - Posted: 23 Sep 2020 | 18:05:21 UTC

For the k, it might be the odd values 4 < k < 10'000 because that is what we do in PPS (under 1'200) and PPSE (over 1'200). For the n and the depth p, see the post Sub-project "life" expectancy where it says: "Proth Prime Search (Sieve) is currently sieving 6M-9M which will be sieved to 900P. We will then transition to 9M-12M which will be sieved to 1600P."

That is all I know.

/JeppeSN

Bur
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Message 143608 - Posted: 24 Sep 2020 | 6:55:21 UTC - in response to Message 143600.

Ok, thanks. I noticed PPS sieve finds factors relatively often.

I have 1.2 factors per 9E9 primes. With 321 Sv I found 0.016 factors per 1E10 primes.

Since 321 Sv is only at 90P and PPS Sv already at 550P I would assume other way around. Are there that much more candidates in the PPS sieve? 321 Sv had 3E6 candidates a few months back.

Or is it because n-value of PPS Sv is lower? Though large n-value should result in less primes, i.e. more factors.

The 321 Sv stderr output is much more versatile, so that's where I got those stats from. ;)
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Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^8-1979 & 1281979 + 4 (cousin prime)

Ravi Fernando
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Message 143627 - Posted: 24 Sep 2020 | 16:21:29 UTC - in response to Message 143608.

Ok, thanks. I noticed PPS sieve finds factors relatively often.
(...)
Are there that much more candidates in the PPS sieve?

This is the main reason. The current 321 sieve is for k=3, c=+/-1, and n between 25M and 50M. That's 50M candidates before sieving. The current PPS sieve is for 5<=k<=9999 (odd), c=+1, and n between 6M and 9M. That's almost 15B candidates before sieving. More candidates means more chances to find a factor. (It would also mean much longer runtime, except that the sieving many k at once lets you speed things up on a GPU.)

The size of the primes used for sieving also makes a difference (smaller primes, more factors). This works in favor of 321 sieve, as it's around 84P vs. 563P. But the size of the numbers being sieved doesn't matter. For example: what's the probability that a random 1M-digit number is divisible by p=8675309? Answer: 1/p. What about a 10M digit number? Answer: still 1/p.

It's true that primes are rarer among larger numbers, but only because they have more potential (very large) factors. If a 1M-digit number has no factors below 500K digits, then it's prime. But a 10M-digit number could be the product of a 1M-digit prime, a 3M-digit prime, and a 6M-digit prime. This kind of factorization will never be picked up in our sieving.

Message boards : Proth Prime Search : n and k ranges for PPS SV?