A057220 Numbers k such that 2^k - 23 is prime.

2, 4, 6, 8, 12, 14, 18, 36, 68, 152, 212, 324, 1434, 1592, 1668, 3338, 7908, 9662, 27968, 28116, 33974, 41774, 66804, 144518, 162954, 241032, 366218, 676592, 991968

Offset: 1

Author

Robert G. Wilson v, Sep 16 2000

Keywords

• nonn
• more

Comments

Note that for the values 2 and 4 the primes are negative.

a(22) > 41358. - Jinyuan Wang, Jan 20 2020

All terms are even. - Elmo R. Oliveira, Nov 24 2023

Examples

			k = 6: 2^6 - 23 = 41 is prime.
k = 8: 2^8 - 23 = 233 is prime.
		

Links

• Henri Lifchitz and Renaud Lifchitz, Search for 2^n-23, PRP Top Records.

Crossrefs

Cf. A096502.

Cf. Sequences of numbers k such that 2^k - d is prime: A000043 (d=1), A050414 (d=3), A059608 (d=5), A059609 (d=7), A059610 (d=9), A096817 (d=11), A096818 (d=13), A059612 (d=15), A059611 (d=17), A096819 (d=19), A096820 (d=21), this sequence (d=23), A356826 (d=29).

Programs

Mathematica

Do[ If[ PrimeQ[ 2^n - 23 ], Print[ n ] ], { n, 1, 15000} ]

PARI

is(n)=ispseudoprime(2^n-23) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(19)-a(21) from Jinyuan Wang, Jan 20 2020

a(22)-a(23) found by Henri Lifchitz, a(24)-a(27) found by Lelio R Paula, a(28)-a(29) found by Stefano Morozzi, added by Elmo R. Oliveira, Nov 24 2023