

A088256


Primorial numbers k such that both k1 and k+1 are prime.


4




OFFSET

1,1


COMMENTS

Conjecture: sequence is finite.
Search extended to first 3000 primorials.  Josey Stevens, Aug 10 2021
The first more than 230000 primorial numbers k have been checked for whether k1 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



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(P1) then P else NULL fi
end proc:


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(pr1) && isprime(pr+1), print1(pr, ", "))); \\ Michel Marcus, Aug 31 2016


CROSSREFS



KEYWORD

more,nonn,bref


AUTHOR



EXTENSIONS



STATUS

approved



