A046268 Largest prime substring in 2^n (or 0 if none exist).

0, 2, 0, 0, 0, 3, 0, 2, 5, 5, 2, 2, 409, 19, 163, 7, 6553, 131, 2621, 5, 857, 971, 419, 83, 1677721, 5443, 71, 1342177, 43, 709, 107, 83, 4294967, 89, 171798691, 3597383, 6871947673, 3743895347, 779069, 54975581, 511627, 99023, 4398046511, 79609, 18604441, 883

Offset: 0

Author

Patrick De Geest, Jun 15 1998

Keywords

• nonn

Examples

			2^37 = 1{3743895347}2, so a(37) = 3743895347.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A000079, A046260, A047814.

Programs

Python

from sympy import isprime
def a(n):
    s = str(2**n)
    ss = (int(s[i:j]) for i in range(len(s)) for j in range(i+1, len(s)+1))
    return max((k for k in ss if isprime(k)), default=0)
print([a(n) for n in range(46)]) # Michael S. Branicky, Sep 20 2022

Formula

a(n) = A047814(2^n). - Pontus von Brömssen, Jan 16 2025

Extensions

a(44) and beyond from Michael S. Branicky, Sep 20 2022