This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
k = 3 is here because 5*3! + 1 = 31 is prime.
is(k) = ispseudoprime(5*k!+1); \\ Jinyuan Wang, Feb 04 2020
lst={};Do[p=2*n!+1;If[PrimeQ[p],AppendTo[lst,p]],{n,0,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 28 2009 *)
Select[2*Range[200]!+1,PrimeQ] (* Harvey P. Dale, Oct 26 2013 *)
for(n=1,55, if(isprime(2*n!+1),print(2*n!+1)))
{ n=0; f=1; for (m=1, 10^5, f*=m; if(isprime(a=2*f + 1), write("b062698.txt", n++, " ", a); if (n==12, break)) ) } \\ Harry J. Smith, Aug 09 2009
5 is in the sequence because 2*(2*3*5*7*11) + 1 = 4621 is prime.
Position[2#+1&/@FoldList[Times,Prime[Range[800]]],?PrimeQ]//Flatten (* _Harvey P. Dale, Oct 09 2018 *)
isok(k) = isprime(1+2*prod(j=1, k, prime(j))); \\ Michel Marcus, May 28 2018
from sympy import isprime, nextprime
def afind(limit):
p, primorialk = 2, 2
for k in range(1, limit+1):
if isprime(2*primorialk + 1):
print(k, end=", ")
p = nextprime(p)
primorialk *= p
afind(400) # Michael S. Branicky, Dec 24 2021
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