

A147517


Number of pairs of primes p < q such that (p+q)/2 = A002110(n), the nth primorial.


2



0, 1, 6, 30, 190, 1564, 17075, 226758, 3792532, 82116003, 1975662890
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OFFSET

1,3


COMMENTS

The sequence is infinite and illustrates the number of primes expected to be centered around a given primorial.
Given everincreasing primorial P, one can expect to find the highest symmetrical prime just below 2P.
Using a limited dataset, the approximate relation is the quadratic Y=Ax^2+Bx+C (A,B,C)=(0.12267, 0.75758, 1.592) where Y = log(number of prime pairs) (each > the prime factors) and x is number of prime factors of the seed primorial.


LINKS



FORMULA



EXAMPLE

There are 6 pairs centered at primorial=30: (29,31),(23,37),(19,41),(17,43),(13,47),(7,53). As they are symmetrical, each prime pair sums to twice the primorial center.


MATHEMATICA

f = Compile[{{n, _Integer}}, Block[{p = 2, c = 0, pn = Times @@ Prime@ Range@ n}, While[p < pn, If[PrimeQ[ 2pn p], c++]; p = NextPrime@ p]; c]]; Array[f, 10] (* Robert G. Wilson v, Feb 08 2018 *)


PROG

(PARI) a(n) = pn = prod(k=1, n, prime(k)); nb = 0; forprime(p=2, pn1, if (isprime(2*pnp), nb++)); nb; \\ Michel Marcus, Jul 09 2017


CROSSREFS



KEYWORD

more,nonn


AUTHOR



EXTENSIONS

Typo corrected typo by T. D. Noe, Nov 10 2008


STATUS

approved



