A097223 Prime numbers p such that p = prime(n) and n = product of the digits of p.

17, 73, 2475989

Offset: 1

Author

Farideh Firoozbakht, Aug 06 2004

Keywords

• base
• fini
• full
• nonn
• bref

Comments

This sequence is a subsequence of A097220, so the sequence is also a subsequence of A097221.

There is no further term. - Farideh Firoozbakht, Jul 15 2009

Examples

			2475989 is in the sequence because 2475989 is (2*4*7*5*9*8*9)-th prime.
		

Links

• Jessie Byrnes, Chris Spicer and Alyssa Turnquist, The Sheldon Conjecture. Math Horizons, Vol. 23, No. 2 (November 2015), pp. 12-15 (4 pages); alternate link.
• Chris K. Caldwell and G. L. Honaker, Jr., 2475989
• Carl Pomerance, What we still don't know about addition and multiplication, Trjitzinsky Lecture 1, U. Illinois Urbana-Champaign, November 27, 2018. See slides 22 & 24.
• Carl Pomerance and Chris Spicer, Proof of the Sheldon Conjecture, The American Mathematical Monthly, September 2019, 126(8), 688-698; alternate link.

Crossrefs

Cf. A097220, A097221.

Programs

Mathematica

v={}; Do[If[h=IntegerDigits[Prime[n]]; l=Length[h]; p=Product[h[[k]], {k, l}]; p==n, v=Append[v, Prime[n]]; Print[v]], {n, 205000000}]

PARI

isok(p) = isprime(p) && (primepi(p) == vecprod(digits(p))); \\ Michel Marcus, Jan 27 2019