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2011-04-11, 22:12   #47
mdettweiler
A Sunny Moo

Aug 2007
USA (GMT-5)

3·2,083 Posts

Quote:
 Originally Posted by vaughan Hey Gary, Kar_bon or Max how many work units do you need to crunch on "NotVeryManyPrimesLeftBehind" to find one now? I went the whole rally and didn't find one.
For the 7th Drive at current sieve depth and n-level, you can statistically expect one prime every 10,000 candidates tested. That is, after you've tested 10,000 candidates there's a ~62% chance you'll have found a prime. (Gary can explain the mathematical basis for all this in much greater detail than I if you're interested.)

Of course, note that this is just a statistical expectation based on an assumed random distribution of primes; in reality, while this model does fit quite nicely over the big picture, the specific distribution of primes can vary quite a bit. It has been my (and others') observation that primes tend to come in "bunches", i.e. there will often be dense clusters and large droughts rather than a more even distribution; though at this point there is no mathematical basis for this theory and it's just a popular "hunch". Assuming the "bunch theory" is true, then port 9000 happened to hit a few bunches and 3000 hit all the droughts in between. And since you happened to be on port 3000, you were out of luck (as was everybody else on 3000 except Gary and Karsten, who found one prime each and probably came out right on or just a little under the statistical expectation).