A352604 Primes p such that p^2+3*p+1 and p^2+p-1 are also prime.

2, 3, 5, 19, 53, 59, 163, 263, 349, 373, 419, 449, 499, 1013, 1093, 1259, 1303, 1423, 1489, 1493, 1669, 1759, 2069, 2729, 2879, 3463, 3943, 4159, 4243, 4283, 4493, 4603, 4793, 4969, 5113, 5303, 5563, 6323, 6599, 6803, 6829, 6883, 7369, 7523, 7529, 7963, 8039, 8713, 8969, 9043, 9173, 9293, 9623

Offset

1,1

Comments

Primes p such that (p-1)*p+(p-1)+p and p*(p+1)+p+(p+1) are also prime.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 5 is a term because 5, 5^2+3*5+1 = 41 and 5^2+5-1 = 29 are all prime.

Maple

select(t -> isprime(t^2+3*t+1) and isprime(t^2+t-1), [seq(ithprime(i), i=1..10000)]);

Prog

(Python)
from itertools import islice
from sympy import isprime, nextprime
def agen():
    p = 2
    while True:
        if isprime(p**2 + 3*p + 1) and isprime(p**2 + p - 1):
            yield p
        p = nextprime(p)
print(list(islice(agen(), 53))) # Michael S. Branicky, Mar 22 2022

Crossrefs

Intersection of A053184 and A153590.

Sequence in context: A140560 A118625 A031133 * A235622 A235637 A028490

Adjacent sequences: A352601 A352602 A352603 * A352605 A352606 A352607

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Mar 22 2022

Status

approved