This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A360040 #10 Jan 23 2023 09:10:19
%S A360040 2,3,5,7,19,23,29,41,43,47,53,59,61,67,83,89,257,263,269,409,431,487,
%T A360040 523,541,827,829,853,859,2861,4027,4801,5209,5623,5849
%N A360040 Prime numbers missing from A359136: prime numbers for which none of the nontrivial permutations of its digits (permitting leading zeros) produces a prime number.
%C A360040 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.
%C A360040 All terms belong to A360041.
%F A360040 The nontrivial permutations of the digits of 409 (permitting leading zeros) are:
%F A360040 049 = 7^2,
%F A360040 094 = 2 * 47,
%F A360040 490 = 2 * 5 * 7^2,
%F A360040 904 = 2^3 * 113,
%F A360040 940 = 2^2 * 5 * 47,
%F A360040 so 409 belongs to the sequence.
%o A360040 (PARI) is(p) = { my (d=digits(p)); if (#d > #Set(d), return (0), forperm (vecsort(d), t, my (q=fromdigits(Vec(t))); if (p!=q && isprime(q), return (0))); return (1)) }
%Y A360040 Cf. A359136, A359137, A360041.
%K A360040 nonn,base,fini,full
%O A360040 1,1
%A A360040 _Rémy Sigrist_, Jan 23 2023