A155762 Prime numbers p such that prepending any single decimal digit to p does not produce a prime.

2, 5, 149, 401, 509, 773, 809, 1021, 1103, 1289, 1301, 1451, 1697, 1709, 1747, 1877, 1889, 2087, 2389, 2521, 2663, 3373, 3511, 3631, 3733, 3779, 3821, 3919, 3947, 3989, 4003, 4073, 4241, 4289, 4339, 4637, 4643, 4801, 4931, 5039, 5113, 5387, 5417, 5477

Offset: 1

Author

Dmitry Kamenetsky, Jan 26 2009

Keywords

• nonn
• base

Comments

149 is in the sequence, because the following numbers are all composite: 1149, 2149, 3149, 4149, 5149, 6149, 7149, 8149 and 9149.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A119289.

Programs

Mathematica

Select[Prime@Range@1000, NoneTrue[#+10^IntegerLength@#*Range@9, PrimeQ]&] (* Hans Rudolf Widmer, May 28 2022 *)

Python

from sympy import isprime, primerange
def ok(p): return not any(isprime(int(d+str(p))) for d in "123456789")
print(list(filter(isprime, primerange(2, 5500)))) # Michael S. Branicky, May 28 2022