Quote:
Originally Posted by jasong
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 1100M: 7 primes
Range 100M200M: 7 primes
Range 200M300M: 11 primes
Range 300M400M: 13 primes
Range 400M500M: 12 primes
Range 500M600M: 11 primes
Range 600M700M: 8 primes
Range 700M800M: 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 primerich n=344208 theory may be right.
*edit: on average