A245808 -id:A245808 - cp's OEIS frontend

A246043 Biprimatic permutable numbers: Decimal numbers whose digits can be arranged to form exactly two prime numbers. No leading zeros.

13, 17, 31, 37, 71, 73, 79, 97, 107, 118, 119, 124, 125, 127, 128, 133, 139, 142, 146, 152, 164, 169, 170, 172, 181, 182, 191, 193, 196, 214, 215, 217, 218, 238, 239, 241, 251, 271, 277, 281, 283, 293, 313, 319, 328, 329, 331, 346, 347, 349, 356, 364, 365, 367, 368, 374, 376, 382, 386, 391, 392, 394, 412, 416, 421, 436, 437

Offset: 1

Andreas Boe, Aug 23 2014

In base ten these numbers can be said to have a prime twin made up of the same digits.

			170 -> 017 (forbidden), 071 (forbidden), 107 (prime), 170 (even), 701 (prime), 710 (even) -> conclusion: Two prime numbers.

Andreas Boe, Table of n, a(n) for n = 1..14440

A245808: Monoprimatic permutable numbers
A246044: Monoprimatic permutable primes
A246045: Biprimatic permutable primes

Select[Range[500],Count[FromDigits/@Select[Permutations[IntegerDigits[#]], #[[1]] != 0&],?PrimeQ]==2&] (* _Harvey P. Dale, Oct 23 2018 *)

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

Original entry on oeis.org

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

Andreas Boe, Aug 23 2014

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

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)

Cf. A245808 (monoprimatic permutable numbers)

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

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 *)

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

A246045 Biprimatic permutable primes: prime numbers whose digits can be rearranged to form exactly one other prime number. No leading zeros allowed.

Original entry on oeis.org

13, 17, 31, 37, 71, 73, 79, 97, 107, 127, 139, 181, 191, 193, 239, 241, 251, 271, 277, 281, 283, 293, 313, 331, 347, 349, 367, 421, 439, 457, 461, 463, 467, 479, 521, 547, 563, 569, 577, 587, 619, 641, 643, 647, 653, 659, 673, 683, 691, 701, 709, 727, 743, 757, 769, 787, 797, 811, 821, 823, 857, 863, 877, 907, 911, 947, 967

Offset: 1

Andreas Boe, Aug 23 2014

In base ten the numbers can be said to have a prime twin made up of the same digits.

			709 -> 079 (forbidden), 097 (forbidden), 709 (prime), 790 (even), 907 (prime), 970 (even) -> conclusion: Two primes.

Andreas Boe, Table of n, a(n) for n = 1..828

A245808: Monoprimatic permutable numbers
A246044: Monoprimatic permutable primes
A246043: Biprimatic permutable numbers

A248010 Non-primatic permutable numbers: All permutations of the number's digits except the ones resulting in leading zeros are nonprimes.

Original entry on oeis.org

1, 4, 6, 8, 9, 10, 12, 15, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 33, 36, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 75, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 93, 94, 96, 99, 100, 102, 105, 108, 111, 114, 116, 117, 120, 122, 123, 126, 129, 132, 135, 138, 141, 144, 147

Offset: 1

Andreas Boe, Sep 29 2014

This sequence differs slightly from "absolute composite numbers". 30 is not an absolute composite since 03 is counted as a prime, but in this sequence permutations with leading zeros are disqualified as viable permutations.

			7000 qualifies since it is a composite and the only allowed permutation of its four digits.

Andreas Boe, Table of n, a(n) for n = 1..10000

Absolute composites: A067012, A067013.
Monoprimatic permutable numbers: A245808.
Biprimatic permutable numbers: A246043.

cp's OEIS Frontend

A246043 Biprimatic permutable numbers: Decimal numbers whose digits can be arranged to form exactly two prime numbers. No leading zeros.

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

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A246045 Biprimatic permutable primes: prime numbers whose digits can be rearranged to form exactly one other prime number. No leading zeros allowed.

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A248010 Non-primatic permutable numbers: All permutations of the number's digits except the ones resulting in leading zeros are nonprimes.

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