A246044 Monoprimatic permutable primes: Decimal prime numbers whose digits cannot be rearranged to form another prime number. No leading zeros allowed.

2, 3, 5, 7, 11, 19, 23, 29, 41, 43, 47, 53, 59, 61, 67, 83, 89, 101, 103, 109, 151, 211, 223, 227, 229, 233, 257, 263, 269, 307, 353, 383, 401, 409, 431, 433, 443, 449, 487, 499, 503, 509, 523, 541, 557, 599, 601, 607, 661, 677, 773, 809, 827, 829, 853, 859, 881, 883, 887, 929, 997, 1447, 1451, 1481, 2003, 2017, 2029, 2087

Offset: 1

Author

Andreas Boe, Aug 23 2014

Keywords

• nonn
• base

Examples

			859 -> 589 (composite), 598 (even), 859 (prime), 895 (composite), 958 (even), 985 (composite) -> conclusion: one prime number.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..760 (terms < 10^13, terms 1..406 from Andreas Boe, terms 407..538 from Chai Wah Wu)

Crossrefs

Cf. A245808 (monoprimatic permutable numbers)

Cf. A246043 (biprimatic permutable numbers), A246045 (biprimatic permutable primes).

Programs

Mathematica

mppQ[n_]:=Total[Boole[PrimeQ[Select[FromDigits/@Permutations[IntegerDigits[n]],IntegerLength[ #] == IntegerLength[ n]&]]]] ==1; Select[Prime[Range[500]],mppQ] (* Harvey P. Dale, Dec 06 2021 *)

Python

from itertools import permutations
from sympy import prime, isprime
A246044 = []
for n in range(1,10**6):
    p = prime(n)
    for x in permutations(str(p)):
        if x[0] != '0':
            p2 = int(''.join(x))
            if p2 != p and isprime(p2):
                break
    else:
        A246044.append(p) # Chai Wah Wu, Aug 27 2014