Thread: 69 * 2^n - 1
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Old 2015-02-17, 11:38   #51
Thomas11's Avatar
Feb 2003

3·5·127 Posts

Originally Posted by unconnected View Post
Why so much difference between 1M-3M and 4M-6M ranges? Usually difference no more than 5-7%. For example, for k=33:

  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
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