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

[franktaw at netscape.net]

Small prime gaps tend to be 2 or 4, which means that the primes
will not be congruent modulo 3.  After 3 itself, this means that their
product will be 2 mod 3, and so pq-2 will be divisible by 3.

Further, for a prime gap of 6, there is a 2/3 chance that pq-2 will
be divisible by 5.  And gaps of 8 or 10 will again give 3 as a factor.

I would expect this effect to diminish for large primes.  Perhaps by
the time you get to 8 or 10 digit primes, it should be reduced to
the noise level.

Franklin T. Adams-Watters

-----Original Message-----
From: zak seidov <zakseidov at yahoo.com>

Cf. A048797, A051507:

primes of the form pq+2 (p=prime, q=nextprime(p))
are (much) more frequent than
primes of the form pq-2,

or in other words,

A048797(n) >> A051507(n), except the first term.

Any rational explanation? Thx, zak