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A356110
Numbers k such that k^2 + {1,3,7,13,31} are prime.
1
4, 10, 14290, 43054, 109456, 315410, 352600, 483494, 566296, 685114, 927070, 1106116, 1248796, 1501174, 1997986, 2399204, 2501404, 2553100, 2726840, 2874680, 3291760, 4129394, 4473766, 4794520, 4901144, 6350306, 7444070, 7753456, 7892504, 8009536, 8069540
OFFSET
1,1
COMMENTS
Conjecture: the sequence is infinite.
EXAMPLE
4^2 + {1,3,7,13,31} = {17,19,23,29,47} are all prime.
MAPLE
q:= k-> andmap(j-> isprime(k^2+j), [1, 3, 7, 13, 31]):
select(q, [$0..1000000])[]; # Alois P. Heinz, Jul 27 2022
MATHEMATICA
Select[Range[10^6], AllTrue[#^2 + {1, 3, 7, 13, 31}, PrimeQ] &] (* Amiram Eldar, Jul 27 2022 *)
PROG
(Python)
from sympy import isprime
def ok(n): return all(isprime(n*n+i) for i in {1, 3, 7, 13, 31})
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Jul 27 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 27 2022
STATUS
approved