This is very much inspired by this question.

Take the first 26 primes and relate each one to a letter of the alphabet.
On this occasion, you may choose how each number is mapped to each letter (so, for example we may have A=67, B=31, etc) but each letter must be mapped to a distinct prime.
The score of a word is the product of the primes corresponding to the letters (so if we mapped A=31, L=3 then the score of ALL is 31x3x3 = 279)

What is the longest word which scores at most 1,000,000 for some mapping?

  • $\begingroup$ when you say 1000000, is it the sum / product / concatenate of the numbers; If i map the the letter A to 2 and L to 3, do "ALL" = 233, 18 or 8? $\endgroup$
    – Alex
    Nov 12, 2019 at 17:42
  • 1
    $\begingroup$ @Alex My apologies, I've edited to include the scoring of a word. It follows the same rule as the linked question. $\endgroup$
    – hexomino
    Nov 12, 2019 at 17:45
  • $\begingroup$ Thanks hexomino, so the only difference from the Origin question is that you can freely assign the letters to the primes $\endgroup$
    – Alex
    Nov 12, 2019 at 17:54
  • $\begingroup$ @Alex yes, that's right. $\endgroup$
    – hexomino
    Nov 12, 2019 at 18:00
  • $\begingroup$ What counts as a word, exactly? (Which dictionary?) $\endgroup$
    – Deusovi
    Nov 12, 2019 at 18:42

2 Answers 2


Perhaps not best, but it has to be close:

senselessness (13 letters)
s=2, e=3, n=5, l=7
2^6 * 3^4 * 5^2 * 7 = 907,200

  • 2
    $\begingroup$ Computerized search of a dictionary of ~120k commonish words doesn't find anything better. [EDITED to add:] Or anything else equally good. $\endgroup$
    – Gareth McCaughan
    Nov 12, 2019 at 20:47
  • $\begingroup$ Great answer, this is also what I found and, like Gareth, no words match it. I will refrain from green-ticking for a little while, just in case, but I'm pretty sure this is the best that can be done. $\endgroup$
    – hexomino
    Nov 12, 2019 at 23:07

Partial answer:



m = 7
i = 2
s = 3
p = 5


product = 75600 length = 11


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