A243900 Prime p such that p^5 + p^3 + p - 4 and p^5 + p^3 + p + 4 are primes.

3, 5, 19, 23, 277, 751, 1549, 2851, 2963, 3089, 3463, 3511, 4057, 6067, 6619, 7873, 9257, 10937, 11161, 11321, 11483, 12589, 13997, 15139, 25121, 25939, 26113, 26861, 30971, 33889, 37139, 38119, 39251, 39979, 40763, 41851, 42359, 44293, 50753, 50867, 51907, 54331, 54401, 55871, 56921, 58321, 60611, 62459

Offset

1,1

Comments

Intersection of A243898 (Prime p such that p^5 + p^3 + p + 4 is prime) and A243899 (Prime p such that p^5 + p^3 + p - 4 is prime).

Links

Abhiram R Devesh, Table of n, a(n) for n = 1..1000

Example

Prime p = 3 is in this sequence as p^5 + p^3 + p + 4 = 277 (prime) and p^5 + p^3 + p - 4 = 269 (prime).
Prime p = 5 is in this sequence as p^5 + p^3 + p + 4 = 3259 (prime) and p^5 + p^3 + p - 4 = 3251 (prime).

Mathematica

Select[Prime@ Range[10^4], AllTrue[#^5 + #^3 + # + {-4, 4}, PrimeQ] &] (* Michael De Vlieger, Jan 15 2018 *)

Prog

(Python)
import sympy.ntheory as snt
p=1
while p>0:
....p=snt.nextprime(p)
....pp=p+(p**3)+(p**5)-4
....qq=p+(p**3)+(p**5)+4
....if snt.isprime(pp) == True and snt.isprime(qq) == True:
........print(p)

Crossrefs

Cf. A243898, A243899.

Sequence in context: A180931 A118484 A243898 * A095826 A058778 A211439

Adjacent sequences: A243897 A243898 A243899 * A243901 A243902 A243903

Keyword

nonn

Author

Abhiram R Devesh, Jun 14 2014

Status

approved