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Old 2007-12-18, 20:27   #23
gd_barnes
 
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Quote:
Originally Posted by roger View Post
I've been doing this for my searches, using the average increase across a large amount of primes, and it usually comes out pretty close.



This is where the Payam numbers came from, right? By looking at the factors of a series, to learn which k's have certain factors, and eliminating them from the list of especially good k's?

Thanks!

roger

No, I don't think so, Roger. Curtis can chime in if I'm wrong. What I think he's implying is effectively a 'bias' as I have called it. I can state this because him and I talked about this type of thing a while back. It has little to do with how many primes are in a given range. Of course Payam #'s are going to have some of the highest #'s of primes in a given range just like primorals will. But that doesn't make it any faster to find their primes because there are many more candidates to search after sieving.

What he and me and everyone literally is hoping to find is an equation that produces well higher than expected #'s of primes per candidate remaining after sieving to the same depth.

Example:

1. I sieve k=xx for the range of n=200K-600K to P=1T and have 10,000 candidates remaining.

2. I sieve k=yy for the range of n=200K-600K to P=1T and have 20,000 candidates remaining.


What we're looking for here is to find a statistically significant more number of primes per candidate remaining on one equation than the other. And by statistically significant, I mean something outside of 2 standard deviations (sd's) from the norm for a single degree of freedom such as this. (The more equations being compared, the higher the sd's have to be to make it statistically significant.)

So, let's say that given the range searched above, equation 1 has an expection of 50 primes and equation 2 has an expection of 100 primes (due to 2X # of candidates). Now we do the search and end up with 52 and 94. Certinaly we'd have no bias. Sure, we would have more primes in the latter equation but it wouldn't take any more or less time to find each prime in that range for either equation. It would just take us nearly 2X as long to search equation 2. So nothing of signficance there. We could even have 60 primes for #1 and 90 for #2 and that would probably be close to within the norm to be considered statistical 'noise' as Curtis referred to it.

BUT...if equation 1 had 70 primes and equation 2 had 85 primes, THEN we may be on to something. That would be very significant. Even though equation 1 has less primes, that is the one you want to go after because you're actually taking less time to find each prime.

The key is to find an equation that gives a higher than expected # of primes per candidate remaining. Not to find one that gives a high # of primes. The latter just takes longer to search. The first person to come up with this will slowly but surely dominate the top-5000 site and have a much better chance than anyone else of winning $100,000!


Gary

Last fiddled with by gd_barnes on 2007-12-18 at 20:35
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