A356175 Numbers k such that k^2 + {1,3,7,13,163} are prime.
2, 4, 10, 14290, 64390, 74554, 83464, 93460, 132304, 238850, 262630, 277630, 300206, 352600, 376190, 404954, 415180, 610340, 806180, 984686, 1025650, 1047050, 1106116, 1382860, 2014624, 2440714, 2525870, 2538344, 2760026, 2826380, 3145600, 3508586, 3715156
Offset: 1
Keywords
Examples
2 is a term since 2^2 + {1,3,7,13,163} = {5,7,11,17,167} are all primes.
Links
- David A. Corneth, Table of n, a(n) for n = 1..6757 (first 237 terms from Jean-Marc Rebert, terms <= 10^10).
Crossrefs
Programs
-
Maple
q:= k-> andmap(j-> isprime(k^2+j), [1, 3, 7, 13, 163]): select(q, [$0..1000000])[]; # Alois P. Heinz, Jul 28 2022
-
Mathematica
Select[Range[4*10^6], AllTrue[#^2 + {1, 3, 7, 13, 163}, PrimeQ] &] (* Amiram Eldar, Jul 28 2022 *) -
PARI
is(k)=my(v=[1,3,7,13,163],ok=1);for(i=1,#v,if(!isprime(k^2+v[i]),ok=0;break));ok
-
Python
from sympy import isprime def ok(n): return all(isprime(n*n+i) for i in {1,3,7,13,163}) print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Jul 28 2022
Comments