# Implications of the disproof of the “climb-to-a-prime” conjecture

Now that James Davis has found a counter example, 13532385396179, to John Conway's climb-to-a-prime conjecture, I would be interested to learn whether this has any implications of interest in number theory.

• I guess the answer would be no, but demonstrating that might be impossible. Are there any implications of interest in various other puzzles/results involving patterns in base-10 digits of a number? – spin Jun 9 '17 at 15:41
• Do there exist more non-prime fixed points than a heuristic argument would suggest? If so then that might lead to an interesting mathematical insight. – Timothy Chow Jun 9 '17 at 20:28
• 100 years ago, Dudeney noticed $2^59^2=2592$. If only 9 were prime.... – Gerry Myerson Jun 10 '17 at 5:53
• It would be helpful to add the link (cheswick.com/ches/conway1000.pdf) to the list of Conway's problems containing his "climb-to-a-prime conjecture" under number 5. – Taras Banakh Feb 8 '18 at 7:01