A068689 Primes which are a sandwich of numbers made of only one decimal digit between two 9's.

919, 929, 9222229, 9888889, 9222222222229, 9888888888888888888888888888888888888888888888888888888888888888888888889

Offset: 1

Author

Amarnath Murthy, Mar 02 2002

Keywords

• nonn
• base

Comments

Conjecture: Inner digits 1, 2 and 8 are the only repeating digits for which the resulting numbers can be prime for outer digits 9. I.e., 9444..4449, 9555..5559, 9777..7779 are composite. The cases for inner digits 0, 3, 6 and 9 give composite numbers. - Cino Hilliard, Jul 11 2005

a(13) has 1141 digits. - Michael S. Branicky, Jan 28 2023

Links

• Michel Marcus, Table of n, a(n) for n = 1..12

Crossrefs

Cf. A068685, A068687, A068688.

Programs

PARI

lista(nn) = my(list = List(), p); for (n=1, nn, for (k=1, 8, my(d=vector(n, i, k)); d = concat(9, d); d = concat(d, 9); if (ispseudoprime(p=fromdigits(d)), listput(list, p)););); Vec(list); \\ Michel Marcus, Jan 28 2023

Python

from sympy import isprime
from itertools import count, islice
def agen(): yield from (t for i in count(1) for m in "124578" if isprime(t:=int("9" + m*i + "9")))
print(list(islice(agen(), 11))) # Michael S. Branicky, Jan 28 2023

Extensions

More terms from Sascha Kurz, Mar 17 2002