|
|
A243900
|
|
Prime p such that p^5 + p^3 + p - 4 and p^5 + p^3 + p + 4 are primes.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|