A020472 Primes that contain digits 8 and 9 only.

89, 8999, 89899, 89989, 98899, 98999, 99989, 888989, 898889, 989999, 998989, 8888989, 8889889, 8988989, 8989999, 8998889, 8999899, 9888889, 9889889, 9899999, 9989899, 9999889, 88888999, 88898989, 88989899, 89888989, 89889889, 89898889, 89999999, 98888989

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base

Comments

Or, primes with minimal digit 8.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)
• Index to entries about primes with digits in a given set

Crossrefs

Cf. A020449 (digits 0 & 1), ..., A020471 (digits 7 & 9). - M. F. Hasler, Mar 18 2010

Programs

Mathematica

Select[Prime[Range[80000]], Min[IntegerDigits[#]] == 8 &] (* Zak Seidov, May 07 2005 *)
Flatten[Table[Select[FromDigits/@Tuples[{8, 9}, n], PrimeQ], {n, 8}]] (* Vincenzo Librandi, Jul 27 2012 *)

PARI

for(nd=1,9, p=vector(nd,i,10^(nd-i))~; forvec(v=vector(nd,i,[8+(i==nd),9]), isprime(v*p) && print1(v*p","))) \\ M. F. Hasler, Mar 18 2010

Python

from sympy import isprime
from itertools import count, islice, product
def agen(): # generator of terms
    for d in count(2):
        for first in product("89", repeat=d-1):
            t = int("".join(first) + "9")
            if isprime(t): yield t
print(list(islice(agen(), 30))) # Michael S. Branicky, Nov 15 2022

Extensions

Edited by N. J. A. Sloane, Jan 26 2008 at the suggestion of Lekraj Beedassy