A140315 Numbers n such that n!/n#-1 and n!/n#+1 is a twin prime pair.

4, 5, 8, 34, 280, 281

Offset

4,1

Comments

4,5 and 280,281 result in the same respective twin prime pairs. Using gmp, testing n < 4000, the last 3-prp found was the 8897 digit 3-prp, 3337!/3337#-1.

Links

Table of n, a(n) for n=4..9.

G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 281

Formula

n# is the primorial function A034386(n).

A140293 INTERSECT A140294. - R. J. Mathar, Feb 27 2012

Example

8!/8#-1 = 191,8!/8#-1 = 193. 191 and 193 form a twin prime pair.

Mathematica

Primorial[n_] := Product[Prime[i], {i, 1, PrimePi[n]}];
Select[Range[
  1000], (p = (#! / Primorial[#]);
PrimeQ[p + 1] && PrimeQ[p - 1]) &] (* Robert Price, Oct 11 2019 *)

Prog

(PARI) g(n) = for(x=1, n, y=x!/primorial(x)-1; z=nextprime(y+1); if(ispseudoprime(y)&&z-y==2, print1(x", "))) primorial(n) = \ The product of primes <= n using the pari primelimit. { local(p1, x); if(n==0||n==1, return(1)); p1=1; forprime(x=2, n, p1*=x); return(p1) }

Crossrefs

Sequence in context: A207191 A240790 A229861 * A055497 A194419 A175380

Adjacent sequences: A140312 A140313 A140314 * A140316 A140317 A140318

Keyword

hard,nonn

Author

Cino Hilliard, May 25 2008

Status

approved