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Proth Prime Search :
n and k ranges for PPS SV?
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BurVolunteer tester
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Joined: 25 Feb 20 Posts: 332 ID: 1241833 Credit: 22,611,276 RAC: 4,081

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 & 12^81979 & 1281979 + 4 (cousin prime)  


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 Subproject "life" expectancy where it says: "Proth Prime Search (Sieve) is currently sieving 6M9M which will be sieved to 900P. We will then transition to 9M12M which will be sieved to 1600P."
That is all I know.
/JeppeSN  

BurVolunteer tester
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Joined: 25 Feb 20 Posts: 332 ID: 1241833 Credit: 22,611,276 RAC: 4,081

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 nvalue of PPS Sv is lower? Though large nvalue 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 & 12^81979 & 1281979 + 4 (cousin prime)  

Ravi FernandoProject administrator Volunteer tester Project scientist Send message
Joined: 21 Mar 19 Posts: 144 ID: 1108183 Credit: 8,505,009 RAC: 158

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 1Mdigit 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 1Mdigit number has no factors below 500K digits, then it's prime. But a 10Mdigit number could be the product of a 1Mdigit prime, a 3Mdigit prime, and a 6Mdigit prime. This kind of factorization will never be picked up in our sieving.  

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n and k ranges for PPS SV? 