A053652 Primes for which some rearrangement of the digits (leading zeros not allowed) is the product of two consecutive primes.

53, 233, 347, 431, 743, 1237, 1249, 1327, 1367, 1429, 1471, 1571, 1583, 1637, 1723, 1741, 2137, 2371, 2713, 2731, 3167, 3217, 3271, 3581, 3617, 3671, 3761, 3851, 3863, 3877, 4129, 4219, 5171, 5381, 5399, 5477, 5657, 5711, 5813, 5939, 6173, 6317, 6577, 6833, 7151

Offset

1,1

Comments

Primes from A053736 sorted in numerical order.

References

C. A. Pickover, "Vampire numbers," chapter 30 of Keys to Infinity. NY: Wiley, 1995. Pages 227-231

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

a(3)=347, a(5)=743. These terms are derived from 19*23=437. By arranging digits of 437, two primes are formed: 347 and 743.

Prog

(Python)
from itertools import islice
from sympy import isprime, nextprime
from sympy.utilities.iterables import multiset_permutations
def agen(): # generator of terms
    p, q, terms, digits = 2, 3, set(), 1
    while True:
        s = sorted(str(p*q))
        if len(s) > digits:
            yield from sorted(terms)
            terms, digits = set(), len(s)
        for w in multiset_permutations(s):
            if w[0] != '0' and isprime(t:=int("".join(w))):
                terms.add(t)
        p, q = q, nextprime(q)
print(list(islice(agen(), 45))) # Michael S. Branicky, Jun 12 2026

Crossrefs

Cf. A053736, A053653, A014575.

Sequence in context: A158656 A013536 A142000 * A142316 A390417 A142026

Adjacent sequences: A053649 A053650 A053651 * A053653 A053654 A053655

Keyword

nonn,base,easy,changed

Author

Enoch Haga, Feb 18 2000

Extensions

Edited by Jens Kruse Andersen, Dec 01 2006

a(41) onward from Michael S. Branicky, Jun 12 2026

Status

approved