A073643 Nine-digit primes with all distinct digits.

102345689, 102345697, 102345869, 102346789, 102346879, 102346897, 102346957, 102347689, 102348679, 102348769, 102349867, 102354689, 102354697, 102356489, 102356789, 102356987, 102358769, 102358967, 102364859, 102364879, 102365897

Offset: 1

Author

Zak Seidov, Aug 29 2002

Keywords

• fini
• nonn
• base

Comments

The number of distinct-digit primes are finite. E.g. there are exactly 145227 such nine-digit primes from 102345689 to 987654103.

All terms have exactly one "0" because nine-digit zero-less numbers with all distinct digits are divisible by 9. - Zak Seidov, Mar 15 2015

Examples

			a(1)=102345689 because 102345689 is the smallest 9-digit prime with all distinct digits.
		

Links

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

Crossrefs

For 3-digit distinct-digit primes, see A074675, A074676.

4-digit distinct-digit primes are in A074673, see also A074674.

5-digit distinct-digit primes are in A074671, see also A074672.

6-digit distinct-digit primes are in A074669, see also A074670.

7-digit distinct-digit primes are in A074667, see also A074668.

8-digit distinct-digit primes are in A074665, see also A074666.

Programs

Python

from sympy import isprime
from itertools import permutations as perms
nines = (int("".join(p)) for p in perms("0123456789", 9) if p[0] != "0")
afull = [k for k in nines if isprime(k)]
print(afull[:24]) # Michael S. Branicky, Aug 04 2022