# Goldbach Cryptarithm

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

  PRIME
PRIME
+ PRIME
-------
NUMBER


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

• Do all 8 letters have to be distinct digits?
– smci
Dec 31, 2020 at 9:47
• @smci Yes. That's a common rule for alphametic puzzles. Dec 31, 2020 at 9:54
• @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.
– smci
Dec 31, 2020 at 9:57

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

Also:

Found an alphametic solver for faster solutions.

• 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. Feb 6, 2015 at 10:10

Another solution is:

PRIME = 81957, NUMBER = 245871

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