A088256 - OEIS

%I #48 Mar 31 2023 16:04:36

%S 6,30,2310

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

%C Conjecture: sequence is finite.

%C No more terms in the first 300 primorials. - _David Wasserman_, Jul 25 2005

%C Search extended to first 700 primorials by _Michael De Vlieger_, Aug 31 2016

%C Intersection of A014574 and A002110. - _Michel Marcus_, Dec 03 2016

%C Search extended to first 3000 primorials. - _Josey Stevens_, Aug 10 2021

%C 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

%H Chris K. Caldwell, <a href="https://primes.utm.edu/top20/page.php?id=5">The Top Twenty: Primorial</a>, in the Prime Pages.

%H PrimeGrid, <a href="http://prpnet.primegrid.com:12008/">PRPNet: Primorial Prime Search - Server Statistics</a>.

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

%p f:= proc(n)

%p   local P;

%p   P:= mul(seq(ithprime(i),i=1..n));

%p   if isprime(P+1) and isprime(P-1) then P else NULL fi

%p end proc:

%p map(f, [$1..300]); # _Robert Israel_, Aug 31 2016

%t Select[Times @@ # & /@ Prime@ Range@ Range@ 700, Times @@ Boole@ PrimeQ@ {# - 1, # + 1} == 1 &] (* _Michael De Vlieger_, Aug 31 2016 *)

%t Select[FoldList[Times,Prime[Range[20]]],AllTrue[#+{1,-1},PrimeQ]&] (* _Harvey P. Dale_, Mar 31 2023 *)

%o (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

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

%K more,nonn,bref

%O 1,1

%A _Amarnath Murthy_, Sep 27 2003

%E Corrected by _Ray Chandler_, Sep 28 2003