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.

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

Author

Bernard Schott, Jan 13 2019

Keywords

• nonn
• base
• fini
• full

Comments

There are only 36 terms in this sequence, which is a finite subsequence of A152313.

Two particular examples:

6481 is also the smallest prime formed from the concatenation of two consecutive squares.

81649 is the only prime containing all the nonprime positive digits such that every string of two consecutive digits is a square.

Examples

			14869 is the smallest prime that contains all the nonprime positive digits; 98641 is the largest one.
		

Links

• Chris K. Caldwell and G. L. Honaker, Jr., 81649, Prime Curios!

Crossrefs

Subsequence of A152313. Subsequence of A029743. Subsequence of A155024 (with distinct nonprime digits but with 0) and of A034844.

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).

Programs

Mathematica

Select[Union@ Flatten@ Map[FromDigits /@ Permutations@ # &, Rest@ Subsets@ {1, 4, 6, 8, 9}], PrimeQ] (* Michael De Vlieger, Jan 19 2019 *)

PARI

isok(p) = isprime(p) && (d=digits(p)) && vecmin(d) && (#Set(d) == #d) && (#select(x->isprime(x), d) == 0); \\ Michel Marcus, Jan 14 2019