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Message boards : Project Staging Area : How many PRPNet Genefer Primes?

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Roger
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Message 61660 - Posted: 14 Jan 2013 | 6:06:49 UTC

Found a web site that estimates the number of Generalized Fermat Primes in a sequence:
http://yves.gallot.pagesperso-orange.fr/primes/stat.html

N = 32768
b = 3,093,872 to 5,984,848, primes found by PRPNet = 33
Expected number of GF primes: 33.44 => error = -0.44
Poisson distribution:
Chance of 33 primes: 6.91%
Expected number of GF primes for 6,000,000 < b < 6,100,000 is 1.13

N = 65536
b = 684,736 to 2,894,394, primes found by PRPNet = 12
Expected number of GF primes: 26.37 => error = -14.37
Suspect PRPNet range tested or primes found not correct in stats.
Expected number of GF primes for 2,900,000 < b < 3,000,000 is 1.15

N = 262144
b = 2,900 to 864,200, primes found by PRPNet = 4
Expected number of GF primes: 3.39 => error = -0.61
Poisson distribution:
Chance of 4 primes: 18.54%
Expected number of GF primes for 864,000 < b < 1,000,000 is 0.49

N = 524288
Chance of any GF prime with b > 700,000 doesn't hit 50% till we've tested up to 1,080,000

Playing with the N and b ranges gives you a good idea of expected hit rates. History has shown this estimation to be pretty good.
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Michael Goetz
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Message 61662 - Posted: 14 Jan 2013 | 6:47:46 UTC - in response to Message 61660.