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

6, 30, 2310

Offset

1,1

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

Links

Table of n, a(n) for n=1..3.

Chris K. Caldwell, The Top Twenty: Primorial, in the Prime Pages.

PrimeGrid, PRPNet: Primorial Prime Search - Server Statistics.

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A222718 A200894 A202861 * A136349 A119411 A036285

Adjacent sequences: A088253 A088254 A088255 * A088257 A088258 A088259

Keyword

more,nonn,bref

Author

Amarnath Murthy, Sep 27 2003

Extensions

Corrected by Ray Chandler, Sep 28 2003

Status

approved