A345529 Primes that yield a prime when any single digit is replaced by its 10's complement.

3, 5, 7, 17, 47, 71, 107, 223, 401, 823, 827, 857, 883, 2087, 2089, 2539, 3253, 4007, 5051, 5059, 5503, 5507, 7541, 8447, 10247, 12401, 18041, 25303, 33529, 33589, 35533, 40427, 44171, 45557, 53503, 53653, 53899, 54401, 55001, 55009, 55333, 55817, 57077, 71147, 81017, 82003, 93553

Offset: 1

Author

Lamine Ngom, Jun 20 2021

Keywords

• nonn
• base
• easy

Comments

Digital complement of a digit d is 10-d if d > 0, 0 otherwise.

Primes in A345343.

Examples

			71147 is a term since 31147, 79147, 71947, 71167 and 71143 are all primes.
		

Crossrefs

Cf. A345343, A055120, A089740, A318785.

Programs

Mathematica

q[n_] := PrimeQ[n] && Module[{d = IntegerDigits[n]}, And @@ PrimeQ[Table[ FromDigits[ReplacePart[d, i -> If[d[[i]] == 0, d[[i]], 10 - d[[i]]]]], {i, 1, Length[d]}]]]; Select[Range[10^5], q] (* Amiram Eldar, Jul 06 2021 *)

Python

from sympy import isprime, primerange
def comp(d, i): return d[:i] + str((10-int(d[i]))%10) + d[i+1:]
def ok(p):
    d = str(p)
    return all(isprime(int(comp(d, i))) for i in range(len(d)))
print(list(filter(ok, primerange(1, 95000)))) # Michael S. Branicky, Jun 20 2021