A177061 Primes p formed from single-digit primes only, each used at most once.

2, 3, 5, 7, 23, 37, 53, 73, 257, 523, 2357, 2753, 3257, 3527, 5237, 5273, 7253, 7523

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), May 02 2010

Keywords

• easy
• base
• fini
• full
• nonn

Comments

List of (p,i): (2,1), (3,2), (5,3), (7,4), (23,9), (37,12), (53,16), (73,21), (257,55), (523,99), (2357,350), (2753,402), (3257,460), (3527,492), (5237,697), (5273, 699), (7253,928), (7523,953).

There are exactly eight primes whose digits are primes in strictly increasing order: 2, 3, 5, 7, 23, 37, 257, 2357. - James C. McMahon, Jul 04 2023

There are exactly six primes whose digits are primes in strictly decreasing order: 2, 3, 5, 7, 53, 73. - James C. McMahon, Aug 09 2023

Examples

			3//7 = 37 = prime(12) is the 6th term.
2//3//5//7 = 2357 = prime(350) is the 11th term
p = 7//5//2//3 = 7523 = prime(953) = A033548(59) is the last term.
		

References

• E. I. Ignatjew, Mathematische Spielereien, Urania Verlag Leipzig/Jena/Berlin 1982

Crossrefs

Cf. A000040, A168349, A168385, A347612

Programs

Mathematica

Select[FromDigits/@Flatten[Permutations/@Subsets[{2,3,5,7}],1],PrimeQ]// Union (* Harvey P. Dale, Sep 08 2021 *)

PARI

isok(p) = {my(d = digits(p)); if (#d == #Set(d) && vecmin(apply(isprime, d)) == 1, return (1)); return(0);}
lista() = {forprime(p=1, 100000, if (isok(p), print1(p, ", ")););} \\ Michel Marcus, Aug 07 2020

Extensions

Edited by Assoc. Eds. OEIS, May 09 2010

Missing term 5273 added by Eren Donmez, Aug 07 2020

Cross reference added by Harvey P. Dale, Sep 09 2021