A323391
Primes containing nonprime digits (from 1 to 9) in their decimal expansion and whose digits are distinct, i.e., consisting of only digits 1, 4, 6, 8, 9.
Original entry on oeis.org
19, 41, 61, 89, 149, 419, 461, 491, 619, 641, 691, 941, 1489, 4691, 4861, 6481, 6491, 6841, 8419, 8461, 8641, 8941, 9461, 14869, 46819, 48619, 49681, 64189, 64891, 68491, 69481, 81649, 84691, 84961, 86491, 98641
Offset: 1
14869 is the smallest prime that contains all the nonprime positive digits; 98641 is the largest one.
- Chris K. Caldwell and G. L. Honaker, Jr., 81649, Prime Curios!
Cf.
A029743 (with distinct digits),
A124674 (with distinct prime digits),
A155045 (with distinct odd digits),
A323387 (with distinct square digits),
A323578 (with distinct digits for which parity of digits alternates).
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Select[Union@ Flatten@ Map[FromDigits /@ Permutations@ # &, Rest@ Subsets@ {1, 4, 6, 8, 9}], PrimeQ] (* Michael De Vlieger, Jan 19 2019 *)
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isok(p) = isprime(p) && (d=digits(p)) && vecmin(d) && (#Set(d) == #d) && (#select(x->isprime(x), d) == 0); \\ Michel Marcus, Jan 14 2019
A323579
Primes formed by using the four terminal digits of multidigit primes and whose digits are distinct, i.e., consisting of only digits 1, 3, 7, 9.
Original entry on oeis.org
3, 7, 13, 17, 19, 31, 37, 71, 73, 79, 97, 137, 139, 173, 179, 193, 197, 317, 379, 397, 719, 739, 937, 971, 1973, 3719, 3917, 7193, 9137, 9173, 9371
Offset: 1
1973 and 9371 are respectively the smallest and the largest primes formed with the four digits that can end multidigit primes.
- Chris K. Caldwell and G. L. Honaker, Jr., 9371, Prime Curios!
Cf.
A029743 (with distinct digits),
A124674 (with distinct prime digits),
A155024 (with distinct nonprime digits but with 0),
A155045 (with distinct odd digits),
A323387 (with distinct square digits),
A323391 (with distinct nonprime digits),
A323578 (with distinct digits for which parity of digits alternates).
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With[{w = Select[Range@ 10, GCD[#, 10] == 1 &]}, Select[FromDigits /@ Permutations[w, Length@ w], PrimeQ]] (* Michael De Vlieger, Feb 03 2019 *)
Select[FromDigits/@Flatten[Permutations/@Subsets[{1,3,7,9}],1],PrimeQ]//Union (* Harvey P. Dale, Apr 20 2025 *)
Showing 1-2 of 2 results.
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