A088256 Primorial numbers k such that both k-1 and k+1 are prime.

6, 30, 2310

Offset: 1

Author

Amarnath Murthy, Sep 27 2003

Keywords

• more
• nonn
• bref

Comments

Conjecture: sequence is finite.

No more terms in the first 300 primorials. - David Wasserman, Jul 25 2005

Search extended to first 700 primorials by Michael De Vlieger, Aug 31 2016

Intersection of A014574 and A002110. - Michel Marcus, Dec 03 2016

Search extended to first 3000 primorials. - Josey Stevens, Aug 10 2021

The first more than 230000 primorial numbers k have been checked for whether k-1 or k+1 or both are primes. See links. If another term k exists, it is over about 10^1400000. - Jeppe Stig Nielsen, Oct 19 2021

Examples

			210 = primorial(4) is not a member as 209 is composite.
		

Links

• Chris K. Caldwell, The Top Twenty: Primorial, in the Prime Pages.
• PrimeGrid, PRPNet: Primorial Prime Search - Server Statistics.

Crossrefs

Cf. A001097, A002110, A088257, A014574, A119411, A136349.

Programs

Maple

f:= proc(n)
  local P;
  P:= mul(seq(ithprime(i),i=1..n));
  if isprime(P+1) and isprime(P-1) then P else NULL fi
end proc:
map(f, [$1..300]); # Robert Israel, Aug 31 2016

Mathematica

Select[Times @@ # & /@ Prime@ Range@ Range@ 700, Times @@ Boole@ PrimeQ@ {# - 1, # + 1} == 1 &] (* Michael De Vlieger, Aug 31 2016 *)
Select[FoldList[Times,Prime[Range[20]]],AllTrue[#+{1,-1},PrimeQ]&] (* Harvey P. Dale, Mar 31 2023 *)

PARI

lista(nn) = for (n=1, nn, pr = prod(i=1, n, prime(i)); if (isprime(pr-1) && isprime(pr+1), print1(pr, ", "))); \\ Michel Marcus, Aug 31 2016

Extensions

Corrected by Ray Chandler, Sep 28 2003