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

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Profile BurProject donor
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Joined: 25 Feb 20
Posts: 223
ID: 1241833
Credit: 13,092,890
RAC: 135,445
321 LLR Gold: Earned 500,000 credits (538,216)Cullen LLR Gold: Earned 500,000 credits (624,600)ESP LLR Gold: Earned 500,000 credits (636,842)PPS LLR Gold: Earned 500,000 credits (837,557)PSP LLR Silver: Earned 100,000 credits (209,588)SR5 LLR Gold: Earned 500,000 credits (531,229)SGS LLR Amethyst: Earned 1,000,000 credits (1,022,026)TRP LLR Gold: Earned 500,000 credits (561,429)Woodall LLR Gold: Earned 500,000 credits (781,741)321 Sieve Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Amethyst: Earned 1,000,000 credits (1,045,010)AP 26/27 Ruby: Earned 2,000,000 credits (2,470,273)GFN Amethyst: Earned 1,000,000 credits (1,718,686)PSA Bronze: Earned 10,000 credits (10,909)
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?
____________
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)

Profile JeppeSNProject donor
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Joined: 5 Apr 14
Posts: 1280
ID: 306875
Credit: 17,941,064
RAC: 30,733
Found 1 prime in the 2020 Tour de Primes321 LLR Gold: Earned 500,000 credits (529,293)Cullen LLR Bronze: Earned 10,000 credits (98,851)ESP LLR Silver: Earned 100,000 credits (139,922)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (35,236)PPS LLR Turquoise: Earned 5,000,000 credits (8,175,730)PSP LLR Silver: Earned 100,000 credits (212,242)SoB LLR Silver: Earned 100,000 credits (237,390)SR5 LLR Silver: Earned 100,000 credits (145,419)SGS LLR Silver: Earned 100,000 credits (104,534)TRP LLR Silver: Earned 100,000 credits (342,501)Woodall LLR Silver: Earned 100,000 credits (109,455)321 Sieve Silver: Earned 100,000 credits (175,037)AP 26/27 Bronze: Earned 10,000 credits (12,129)PSA Turquoise: Earned 5,000,000 credits (7,614,290)
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

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Joined: 25 Feb 20
Posts: 223
ID: 1241833
Credit: 13,092,890
RAC: 135,445
321 LLR Gold: Earned 500,000 credits (538,216)Cullen LLR Gold: Earned 500,000 credits (624,600)ESP LLR Gold: Earned 500,000 credits (636,842)PPS LLR Gold: Earned 500,000 credits (837,557)PSP LLR Silver: Earned 100,000 credits (209,588)SR5 LLR Gold: Earned 500,000 credits (531,229)SGS LLR Amethyst: Earned 1,000,000 credits (1,022,026)TRP LLR Gold: Earned 500,000 credits (561,429)Woodall LLR Gold: Earned 500,000 credits (781,741)321 Sieve Ruby: Earned 2,000,000 credits (2,107,153)PPS Sieve Amethyst: Earned 1,000,000 credits (1,045,010)AP 26/27 Ruby: Earned 2,000,000 credits (2,470,273)GFN Amethyst: Earned 1,000,000 credits (1,718,686)PSA Bronze: Earned 10,000 credits (10,909)
Message 143608 - Posted: 24 Sep 2020 | 6:55:21 UTC - in response to Message 143600.
Last modified: 24 Sep 2020 | 7:06:05 UTC

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. ;)
____________
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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Joined: 21 Mar 19
Posts: 123
ID: 1108183
Credit: 8,173,359
RAC: 20,185
321 LLR Silver: Earned 100,000 credits (370,134)Cullen LLR Bronze: Earned 10,000 credits (18,910)ESP LLR Bronze: Earned 10,000 credits (16,570)Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (12,551)PPS LLR Ruby: Earned 2,000,000 credits (2,042,311)PSP LLR Bronze: Earned 10,000 credits (26,371)SoB LLR Silver: Earned 100,000 credits (183,524)SR5 LLR Bronze: Earned 10,000 credits (59,307)SGS LLR Silver: Earned 100,000 credits (148,878)TRP LLR Silver: Earned 100,000 credits (195,905)Woodall LLR Bronze: Earned 10,000 credits (19,925)321 Sieve Turquoise: Earned 5,000,000 credits (5,001,667)AP 26/27 Bronze: Earned 10,000 credits (72,774)
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.

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

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