A360041 Prime numbers missing from A359137: prime numbers for which none of the nontrivial permutations of its digits (not permitting leading zeros) produces a prime number.

2, 3, 5, 7, 19, 23, 29, 41, 43, 47, 53, 59, 61, 67, 83, 89, 103, 109, 257, 263, 269, 307, 401, 409, 431, 487, 503, 509, 523, 541, 601, 607, 809, 827, 829, 853, 859, 2017, 2087, 2861, 4027, 4051, 4079, 4801, 5021, 5209, 5623, 5849, 6047, 6053, 6803, 8053, 8059

Offset

1,1

Comments

Any prime number p >= 10^11 has necessarily a duplicate digit, say that appears at positions i and j. Applying the nontrivial permutation (i j) to the digits of p yields a prime number (p itself), hence p does not belong to the sequence and the sequence is finite.

Links

Table of n, a(n) for n=1..53.

Example

The nontrivial permutations of the digits of 607 (not permitting leading zeros) are:
  670 = 2 * 5 * 67,
  706 = 2 * 353,
  760 = 2^3 * 5 * 19,
so 607 belongs to the sequence.

Prog

(PARI) is(p) = { my (d=digits(p)); if (#d > #Set(d), return (0), forperm (vecsort(d), t, if (t[1], my (q=fromdigits(Vec(t))); if (p!=q && isprime(q), return (0)))); return (1)) }

Crossrefs

Cf. A359136, A359137, A360040.

Sequence in context: A336446 A129693 A153590 * A360040 A244529 A332583

Adjacent sequences: A360038 A360039 A360040 * A360042 A360043 A360044

Keyword

nonn,base,fini,full

Author

Rémy Sigrist, Jan 23 2023

Status

approved