[seqfan] Re: Primes of the form pq+-2.
franktaw at netscape.net
franktaw at netscape.net
Tue Nov 11 08:27:18 CET 2008
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
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