7

A Gisella prime is a prime number obtained from concatenating the first $n$ natural numbers starting from $2$ and then replace each composite on that concatenation with the concatenation of its prime factors in ascending order, i.e: $23456789101112$ transformed to $23225237222332511223$. The first two Gisella primes are $2$ and $23$. I have checked $n$ up to $1000$, but I couldn't find other primes. Could you find the third Gisella prime?

Michael Hardy
  • 1
Gisella M
  • 79
  • Quite a difficult problem, and the OEIS is of little help here. 2, 23 gives way too many results. – Robert Soupe Aug 10 '15 at 01:38
  • No solutions below $2500$. – Lucian Aug 10 '15 at 02:15
  • Why did you choose to start concatenating numbers from 2 and not from 1? – rywit Aug 10 '15 at 13:06
  • 1
    @RobertSoupe the sequences $2,23,2322,23225...$ and $1,12,123,12322...$ are not in the OEIS so I think it's safe to assume that the one containing only primes isn't either – Alessandro Codenotti Aug 10 '15 at 23:27
  • If we start with 1 then we get 6 (12322523), 27, 53, 2179, 3539. Nothing else to 4200. Starting with 2, nothing past 2 and 23 out to 12400.

    Starting at two makes sense, as factor(1) returns the empty set in most systems.

     – DanaJ Aug 11 '15 at 06:05

0 Answers0