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Old 2008-10-01, 06:34   #6
Apprentice Crank
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Mar 2006

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Originally Posted by jasong View Post
The person who picked n=344,208 used number theory to pick that n, he decided that that would be a better number than n=333,333, which is what the starter of the twin prime project picked. My friend said that, statistically speaking, n=344,208 was tremendously likely to yield a prime within a given amount of time than n=333,333, assuming the same amount of crunching time.
I doubt the person who suggested n=344208 is right, but there's an easy way to find out. Sieve a 100M range for twins to at least 50T, and count the number of single primes you find in that range after LLRing it.

For comparision, here's the stats for n=333,333:

Range 1-100M: 7 primes
Range 100M-200M: 7 primes
Range 200M-300M: 11 primes
Range 300M-400M: 13 primes
Range 400M-500M: 12 primes
Range 500M-600M: 11 primes
Range 600M-700M: 8 primes
Range 700M-800M: 12 primes

As you can see, there are about 10 primes per 100M* for n=333,333. If you find close to 20 primes for your 100M range, then the prime-rich n=344208 theory may be right.

*edit: on average

Last fiddled with by MooooMoo on 2008-10-01 at 06:35
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