A349636 Primes that remain prime when a single "1" digit is inserted between any two adjacent digits.

13, 31, 37, 67, 79, 103, 109, 151, 163, 181, 193, 211, 241, 367, 457, 547, 571, 601, 613, 631, 709, 787, 811, 1117, 1213, 1831, 2017, 2683, 3019, 3319, 3391, 3511, 3517, 3607, 4519, 4999, 6007, 6121, 6151, 6379, 6673, 6871, 6991, 8293, 11119, 11317, 11467

Offset: 1

Author

Michael S. Branicky, Nov 23 2021

Keywords

• nonn
• base

Examples

			37 and 317 are prime; 2683 is prime, as are 21683, 26183, and 26813.
		

Links

• Martin Ehrenstein, Table of n, a(n) for n = 1..2004

Crossrefs

The terms of A069246 > 10 are a subsequence.

Cf. A215417 (same with 0), A217044 (2), A217045 (4), A217046 (6), A217047 (8), A217062 (9), A217063 (3), A217064 (5), A217065 (7).

Subsequence of A002476.

Programs

Mathematica

Select[Prime@Range[5,1500],(p=#;And@@PrimeQ[FromDigits/@(Insert[IntegerDigits@p,1,#]&/@Range[2,IntegerLength@p])])&] (* Giorgos Kalogeropoulos, Nov 23 2021 *)

Python

from sympy import isprime, primerange
def ok(p):
    if p < 10: return False
    s = str(p)
    return all(isprime(int(s[:i] + "1" + s[i:])) for i in range(1, len(s)))
def aupto(limit): return [p for p in primerange(1, limit+1) if ok(p)]
print(aupto(12000)) # Michael S. Branicky, Nov 23 2021