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A360040
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Prime numbers missing from A359136: prime numbers for which none of the nontrivial permutations of its digits (permitting leading zeros) produces a prime number.
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1
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2, 3, 5, 7, 19, 23, 29, 41, 43, 47, 53, 59, 61, 67, 83, 89, 257, 263, 269, 409, 431, 487, 523, 541, 827, 829, 853, 859, 2861, 4027, 4801, 5209, 5623, 5849
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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The nontrivial permutations of the digits of 409 (permitting leading zeros) are:
049 = 7^2,
094 = 2 * 47,
490 = 2 * 5 * 7^2,
904 = 2^3 * 113,
940 = 2^2 * 5 * 47,
so 409 belongs to the sequence.
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PROG
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(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)) }
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CROSSREFS
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KEYWORD
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nonn,base,fini,full
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AUTHOR
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STATUS
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approved
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