A159292 Pandigital emirps.

10124389567, 10124563789, 10124597683, 10124635897, 10124673859, 10124687359, 10124695783, 10124735689, 10124795683, 10124867359, 10124958673, 10124965387, 10124965783, 10125364897, 10125693847, 10125749863, 10125784639, 10125938467, 10126387549, 10126457893, 10126498573

Offset: 1

Author

Lekraj Beedassy, Apr 08 2009

Keywords

• nonn
• base

Comments

There are 413842 11-digit terms. - Jud McCranie, Jul 03 2013 [in light of the comment below, this was independently computed and confirmed to be correct by Michael S. Branicky, Apr 06 2024]

The above statement [by Jud McCranie] is uncertain, as the contributed b-file was wrong (missing terms) from a(436) on. At this point, one has to consider permutations of 10223456789, before coming back, for n > 495, to permutations of 10123456789 starting with 10231.... - M. F. Hasler, Apr 06 2024

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..435 from Jud McCranie, terms 436..500 corrected and added by M. F. Hasler)

Crossrefs

Cf. A006567 (emirps), A050288 (pandigital primes).

Programs

PARI

L=List(); append(N=10123456789, M=Vecsmall([2,3,3]))=forperm(digits(N),p, cmp(p[3..5],M)>0 && break; isprime(P=fromdigits(Vec(p)))&& isprime(fromdigits(Vecrev(p)))&& listput(L, P))
append(); append(10223456789); #A159292=Set(L) \\ M. F. Hasler, Apr 05 2024

Python

from sympy import isprime
from itertools import count, islice, product
def emirp(s):
    r = s[::-1]
    return r != s and isprime(int(s)) and isprime(int(r))
def agen(): # generator of terms
    for d in count(11):
        for f in "1379":
            for m in product("0123456789", repeat=d-2):
                for e in "1379":
                    t = f + "".join(m) + e
                    if len(set(t)) == 10 and emirp(t):
                        yield int(t)
print(list(islice(agen(), 100))) # Michael S. Branicky, Apr 09 2024

Formula

Intersection of A006567 and A050288. - M. F. Hasler, Apr 05 2024

Extensions

Erroneous terms corrected and more terms from M. F. Hasler, Apr 05 2024