A360040 -id:A360040 - cp's OEIS frontend

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

Rémy Sigrist, Jan 23 2023

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.

			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.

Cf. A359136, A359137, A360040.

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)) }

cp's OEIS Frontend

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.

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