Thread: 69 * 2^n - 1 View Single Post
2015-02-17, 11:38   #51
Thomas11

Feb 2003

1,901 Posts

Quote:
 Originally Posted by unconnected Why so much difference between 1M-3M and 4M-6M ranges? Usually difference no more than 5-7%. For example, for k=33: Code: 45919 1M/t17_b2_k33.npg 46129 2M/t17_b2_k33.npg 46271 3M/t17_b2_k33.npg 44182 4M/t17_b2_k33.npg 43896 5M/t17_b2_k33.npg 43877 6M/t17_b2_k33.npg
1M-3M was sieved to p=100P, while 4M-6M has been sieved to p=400P.

The number of factors for a given sieve range (from p1 to p2) can be estimated by N1*(1-log(p1)/log(p2)), where N1 is the number of candidates at sieve level p1. Then the number of candidates surviving the sieve up to p2 should be roughly N2 = N1*log(p1)/log(p2).

By taking N1=46000 at p1=100P (=100*10^15) we get N2=44427 at p2=400P.
This makes the counts given above for k=33 (and all the other k's except k=5) quite plausible for me...

Last fiddled with by Thomas11 on 2015-02-17 at 11:58