[seqfan] Re: Primes of the form pq+-2.

[Richard Mathar]

zs> From: zak seidov <zakseidov at yahoo.com>
zs> 
zs> Cf. A048797, A051507:
zs> 
zs> primes of the form pq+2 (p=prime, q=nextprime(p))
zs> are (much) more frequent than
zs> primes of the form pq-2,
zs> 
zs> or in other words,
zs> 
zs> A048797(n) >> A051507(n), except the first term.
zs> 
zs> Any rational explanation? Thx, zak

The bias of A048797-A051507 is growing like a power law at higher counts.
If the first column below is a limit k, the second column is the count of
primes p<k such that p is in A048797, the 3rd column is the count of primes p<k
such that p is in A051507, and the 4th column is the difference between 
the 2nd and 3rd:

2000 11 36 -25
50000 199 393 -194
100000 359 669 -310
300000 965 1580 -615
500000 1552 2391 -839
1000000 2894 4329 -1435
2000000 5336 7755 -2419
3000000 7665 10870 -3205
5000000 12016 16908 -4892
10000000 22454 30581 -8127
20000000 41846 55800 -13954
25000000 51167 67887 -16720
30000000 60108 79674 -19566
40000000 77968 102438 -24470
50000000 95359 124525 -29166
60000000 112628 146037 -33409
70000000 129451 167319 -37868

The absolute value of the last column grows approximately proportional
to exp(0.774*k) if we fit on a double-logarithmic
scale in the range k>=100000.

Richard J. Mathar