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A097223 Prime numbers p such that p = prime(n) and n = product of the digits of p. 10

%I #11 Jan 27 2019 05:43:22

%S 17,73,2475989

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

%C This sequence is a subsequence of A097220, so the sequence is also a subsequence of A097221. Next term if it exists is greater than 4333000000.

%C There is no further term. [_Farideh Firoozbakht_, Jul 15 2009]

%H Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php?short=2475989">2475989</a>

%H Carl Pomerance, <a href="https://www.math.dartmouth.edu/~carlp/illinoistalk1.pdf">What we still don't know about addition and multiplication</a>, Trjitzinsky Lecture 1, U. Illinois Urbana-Champaign, November 27, 2018. See slides 22 & 24.

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

%t 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}]

%o (PARI) isok(p) = isprime(p) && (primepi(p) == vecprod(digits(p))); \\ _Michel Marcus_, Jan 27 2019

%Y Cf. A097220, A097221.

%K base,fini,full,nonn,bref

%O 1,1

%A _Farideh Firoozbakht_, Aug 06 2004

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