A335361 Prime numbers p such that p!*i + 1 is composite for i = 1..p.

67, 157, 269, 379, 419, 443, 449, 509, 541, 577, 743, 769, 859, 863, 929, 937, 1009, 1087, 1163, 1213, 1217, 1367, 1381, 1481, 1579, 1733, 1747, 1753, 1783, 1787, 1877, 1901, 1997, 2153

Offset: 1

Author

Chai Wah Wu, Jun 10 2020

Keywords

• nonn
• more

Comments

Primes in A335233.

Crossrefs

Cf. A035093, A321805, A335233.

Programs

Mathematica

Select[Prime@ Range@ 100, (f = #!; NoneTrue[f*Range[#] + 1, PrimeQ ]) &] (* Robert Price, Sep 14 2020 *)

PARI

is(p) = if(isprime(p), for(i=1, p, if(ispseudoprime(i*p!+1), return(0))); 1, 0); \\ Jinyuan Wang, Jun 21 2020

Python

from sympy import isprime, nextprime, factorial
A335361_list, p = [], 2
while p < 500:
    f, g = factorial(p), 1
    for i in range(1,p+1):
        g += f
        if isprime(g):
            break
    else:
        A335361_list.append(p)
    p = nextprime(p)

Extensions

a(34) from Jinyuan Wang, Jun 21 2020