A068160 Smallest prime beginning and ending in exactly n 1's and containing at least one digit != 1.

2, 101, 11311, 1114111, 111181111, 111110611111, 1111118111111, 111111151111111, 111111110911111111, 11111111128111111111, 111111111161111111111, 111111111110911111111111, 11111111111104111111111111, 1111111111111031111111111111, 11111111111111611111111111111, 11111111111111173111111111111111

Offset: 0

Author

Amarnath Murthy, Feb 24 2002

Keywords

• nonn
• base

Comments

a(499) has 1001 digits. - Michael S. Branicky, Oct 02 2024

Examples

			a(2) = 11311 is a prime that starts with 11 and ends in 11 (two 1's).
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..498

Crossrefs

Cf. A366416.

Programs

Python

from gmpy2 import is_prime
def a(n):
    suffix, d = (10**n-1)//9, 2*n+1
    while True:
        prefix = 10**(d-n)*suffix
        for mid in range(0, 10**(d-n), 10**n):
            s = str(mid//10**n)
            if s[0] == "1" or s[-1] == "1": continue
            t = prefix + mid + suffix
            if is_prime(t): return t
        d += 1
print([a(n) for n in range(16)]) # Michael S. Branicky, Oct 02 2024

Extensions

Corrected and extended by Sascha Kurz, Jan 03 2003

More precise name and more terms from Hugo Pfoertner, Oct 11 2023

a(0) = 2 inserted by Michael S. Branicky, Oct 02 2024