A050288 Pandigital primes.

10123457689, 10123465789, 10123465897, 10123485679, 10123485769, 10123496857, 10123547869, 10123548679, 10123568947, 10123578649, 10123586947, 10123598467, 10123654789, 10123684759, 10123685749, 10123694857, 10123746859, 10123784569, 10123846597, 10123849657, 10123854679

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• base

Comments

Digits may appear multiple times; density n/log n (almost all primes are pandigital).

Note that actually a(n) is much larger than n*log(n) (see Formula section). Even for n = 10000, a(n) = 111571*n*log(n). - Zak Seidov, Jul 27 2014

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000.
• Eric Weisstein's World of Mathematics, "Pandigital Number".

Crossrefs

Cf. A050278.

Programs

Mathematica

ta={{0}};Do[u=Union[IntegerDigits[n]]; If[Equal[u, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}]&&PrimeQ[n], ta=Append[ta, n]], {n, 10123456789, 20000000000}];ta (* Labos Elemer *)

PARI

is(n)=isprime(n) && #vecsort(digits(n),,8)>9 \\ Charles R Greathouse IV, May 04 2013

Python

from sympy import isprime
from itertools import count, islice, product
def agen(): # generator of terms
    for d in count(11):
        for f in "123456789":
            for m in product("0123456789", repeat=d-2):
                for e in "1379":
                    t = f + "".join(m) + e
                    if len(set(t)) == 10 and isprime(it:=int(t)):
                        yield it
print(list(islice(agen(), 20))) # Michael S. Branicky, Apr 09 2024

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Sep 14 2012

Intersection of A171102 and A000040. - Charles R Greathouse IV, May 04 2013