A037896 -id:A037896 - cp's OEIS frontend

A182351 Primes of the form n^4 - 6.

619, 1500619, 577200619, 3603000619, 4931550619, 12594450619, 24343800619, 29661450619, 32625390619, 65037750619, 88223850619, 195562950619, 220172100619, 586181640619, 1335469140619, 1659523650619, 2480703750619

Offset: 1

Patrick Devlin, Apr 25 2012

nonn

			619 = 5^4 - 6; 1500619 = 35^4 - 6.

Cf. A037896.

# choose N large, then S is the desired set
f:=n->n^4 - 6:
S:={}:
for n from 0 to N do if(isprime(f(n))) then S:=S union {f(n)}: fi: od:

Select[Range[3,3001,2]^4-6,PrimeQ] (* Harvey P. Dale, Mar 03 2023 *)

A309844 Primes of the form n^4 + n^2 + 3.

Original entry on oeis.org

3, 5, 23, 653, 10103, 83813, 160403, 234743, 280373, 1049603, 3420653, 6252503, 11319863, 52207853, 92246423, 146422103, 174913853, 221548343, 442071653, 479807123, 577224653, 607597853, 655385603, 937921253, 1222865933, 1249233683, 1387525253, 1506177293

Offset: 1

Christopher R. Madan, Aug 19 2019

Digital root of all values > 3 is 5, compare A017221.

Subset of A027753. Subset of A017221.

Cf. A037896, A182344, A182345, A049423.

a = [];
for n = 0:1e3
    x = n.^4+n.^2+3;
    if isprime(x); a = [a,x]; end;
end

f[n_] := n^4 + n^2 + 3; Select[f /@ Range[0, 200], PrimeQ] (* Amiram Eldar, Aug 24 2019 *)

from sympy import isprime
a = []
for n in range(0,1000):
    x = n**4+n**2+3
    if isprime(x):
        a.append(x)

cp's OEIS Frontend

A182351 Primes of the form n^4 - 6.

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