As the apology for the mischievous problem about knights and knaves:


Yeah, this was inspired by the famous (or infamous) Goldbach Conjecture.

  • $\begingroup$ Do all 8 letters have to be distinct digits? $\endgroup$
    – smci
    Dec 31, 2020 at 9:47
  • $\begingroup$ @smci Yes. That's a common rule for alphametic puzzles. $\endgroup$
    – P.-S. Park
    Dec 31, 2020 at 9:54
  • $\begingroup$ @PSPark sometimes it is, sometimes not (obviously not when there are >9 letters involved), but the tag doesn't specify, nor does this question, and you have a second answer with non-distinct digits. $\endgroup$
    – smci
    Dec 31, 2020 at 9:57

2 Answers 2


If PRIME is a prime number, then the solution is:

there is no solution

If PRIME is not a prime number, the solution is:

PRIME = 54328, NUMBER = 162984


Found an alphametic solver for faster solutions.

  • 1
    $\begingroup$ It is usual in these problems that a different letter represents a different digit. Also, a number doesn't start with a zero. On the other side, it wasn't specified that PRIME is a prime. So your last solution can be considered as the only proper solution. $\endgroup$
    – Florian F
    Feb 6, 2015 at 10:10

Another solution is:

PRIME = 81957, NUMBER = 245871

  • 1
    $\begingroup$ Your P and B are the same. $\endgroup$
    – f''
    Mar 3, 2016 at 22:42

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