A378563 Primes that remain prime if any three of their digits are deleted.

2237, 2273, 2333, 2357, 2377, 2557, 2753, 2777, 3253, 3257, 3323, 3373, 3527, 3533, 3557, 3727, 3733, 5227, 5233, 5237, 5273, 5323, 5333, 5527, 5557, 5573, 5737, 7237, 7253, 7333, 7523, 7537, 7573, 7577, 7723, 7727, 7753, 7757, 11113, 11117, 11119, 11131, 11171, 11173, 11197

Offset: 1

Author

Enrique Navarrete, Nov 30 2024

Keywords

• nonn
• base
• less

Comments

Any 4-digit term has all digits prime (cf. A019546).

The corresponding sequence for two digits deleted contains only 18 terms up to 10^100 (Cf. A378081).

Any term >= 10000 must have its last four digits be from {1, 3, 7, 9}. - Michael S. Branicky, Dec 01 2024

Examples

			43117 is in the sequence since upon deleting any three digits we get 43, 31, 11, 17 and 47, all of which are prime.
		

Crossrefs

Cf. A019546, A051362, A378081.

Programs

Python

from sympy import isprime
from itertools import combinations as C
def ok(n):
    if n < 1000 or not isprime(n): return False
    s = str(n)
    return all(isprime(int(t)) for i, j, k in C(range(len(s)), 3) if (t:=s[:i]+s[i+1:j]+s[j+1:k]+s[k+1:])!="")
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Dec 01 2024