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
Programs
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Mathematica
Select[Prime@ Range@ 100, (f = #!; NoneTrue[f*Range[#] + 1, PrimeQ ]) &] (* Robert Price, Sep 14 2020 *)
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PARI
is(p) = if(isprime(p), for(i=1, p, if(ispseudoprime(i*p!+1), return(0))); 1, 0); \\ Jinyuan Wang, Jun 21 2020
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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
Comments