A057736 Primes p such that 2^p + 3 is prime.

2, 3, 7, 67

Offset: 1

Author

G. L. Honaker, Jr., Oct 29 2000

Keywords

• more
• nonn

Comments

The next term p is greater than 100000, corresponding to a prime 2^p + 3 with more than 30000 digits. - Ryan Propper, Aug 24 2005

Next term > 2205444. - Joerg Arndt, Mar 07 2021

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 67, p. 24, Ellipses, Paris 2008.

Crossrefs

Cf. A057737 (the corresponding primes).

Subsequence of A057732.

Programs

Mathematica

Select[Prime[Range[20]],PrimeQ[2^#+3]&] (* Harvey P. Dale, Jun 06 2022 *)

Python

from sympy import isprime, primerange
def afind(limit):
  for p in primerange(2, limit+1):
    if isprime(2**p + 3): print(p, end=", ")
afind(1000) # Michael S. Branicky, Mar 07 2021