A256480 Smallest prime obtained by appending n to a nonzero number with identical digits or 0 if no such prime exists.

0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 211, 0, 113, 0, 0, 0, 317, 0, 419, 0, 421, 0, 223, 0, 0, 0, 127, 0, 229, 0, 131, 0, 233, 0, 0, 0, 137, 0, 139, 0, 241, 0, 443, 0, 0, 0, 347, 0, 149, 0, 151, 0, 353, 0, 0, 0, 157, 0, 359, 0, 461, 0, 163, 0, 0, 0, 167, 0, 269

Offset: 0

Author

Chai Wah Wu, Mar 31 2015

Keywords

• nonn
• base

Comments

a(n) = 0 if n is even or a multiple of 5. Conjecture: all other terms are nonzero. Conjecture verified for n <= 10^7.

"Appending" means "on the right".

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000
• Chai Wah Wu, On a conjecture regarding primality of numbers constructed from prepending and appending identical digits, arXiv:1503.08883 [math.NT], 2015.

Crossrefs

Cf. A090287, A256481.

Programs

Python

from gmpy2 import digits, mpz, is_prime
def A256480(n,limit=2000):
    sn = str(n)
    if not (n % 2 and n % 5):
        return 0
    for i in range(1,limit+1):
        for j in range(1,10):
            si = digits(j,10)*i
            p = mpz(si+sn)
            if is_prime(p):
                return int(p)
    else:
        return 'search limit reached.'