A385711 Primes whose digits are all distinct and pairwise coprime.

2, 3, 5, 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 127, 137, 149, 157, 167, 173, 179, 197, 251, 257, 271, 317, 347, 419, 431, 457, 479, 491, 521, 523, 541, 547, 571, 587, 617, 719, 743, 751, 761, 853, 857, 859, 941, 947, 971, 1237, 1259

Offset: 1

Author

Gonzalo Martínez, Jul 07 2025

Keywords

• nonn
• base
• fini
• full

Comments

This sequence has 252 terms, the last being 95471, which have at most 5 digits. This is because each term has at most one even digit and at most 4 odd digits, since gcd(3, 9) = 3.

All terms are in A038618, since if zero is among the digits of a prime p, then p must have at least 3 digits, where at least one of them is greater than 1, say d, and in such a case gcd(0, d) = d ! = 1.

Examples

			857 is a term since it is prime and gcd(8, 5) = gcd(5, 7) = gcd(8, 7) = 1.
		

Links

• Gonzalo Martínez, Table of n, a(n) for n = 1..252

Crossrefs

Subsequence of A029743.

Cf. A038618.

Programs

Mathematica

Select[Prime[Range[10000]], UnsameQ @@ (d = IntegerDigits[#]) && AllTrue[Subsets[d, {2}], CoprimeQ @@ # &] &] (* Amiram Eldar, Jul 13 2025 *)