A059694 Primes p such that 1p1, 3p3, 7p7 and 9p9 are all primes.

53, 2477, 4547, 5009, 7499, 8831, 9839, 11027, 24821, 26393, 29921, 36833, 46073, 46769, 47711, 49307, 53069, 59621, 64283, 66041, 79901, 84017, 93263, 115679, 133103, 151121, 169523, 197651, 207017, 236807, 239231, 255191, 259949, 265271, 270071, 300431, 330047

Offset: 1

Author

Patrick De Geest, Feb 07 2001

Keywords

• nonn
• base

Comments

All terms == 1 (mod 6). The sequence is apparently infinite. There are 16486 terms up to 10^9. - Zak Seidov, Jan 17 2014

Intersection of A069687, A069688, A069689, and A069690. - Zak Seidov, Jan 17 2014

Examples

			53 is a term because 1531, 3533, 7537 and 9539 are primes.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A059677, A032682, A059693.

Programs

Python

from sympy import isprime, nextprime
from itertools import islice
def agen(): # generator of terms
    p = 2
    while True:
        sp = str(p)
        if all(isprime(int(d+sp+d)) for d in "1379"):
            yield p
        p = nextprime(p)
print(list(islice(agen(), 40))) # Michael S. Branicky, Feb 23 2023