Prime words: CART
A prime word is a word, which its letters, when counting a as 1, B as 2 etc, equals a prime number. For example, the word ON is made up of O(15) and N (14). 14+15=29, which is prime. NO, is also a prime word, since the letters are just in another order.
Using the letters C,A,R,T, how many prime words can you make.
The answer is 0.
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Any word must contain a vowel, so we must have A in the word. Since we cannot obtain a prime "digit sum" of 2 , the prime "digit sum" must be odd, so the word cannot contain the letter C. The only prime that we can obtain by adding 1 and some subset of { 1 8 , 2 0 } is 1 + 1 8 = 1 9 , and neither AR nor RA is a word (although both are abbreviations, for example of chemical elements). This makes the answer 0 .
That said, AR appears in the Scrabble dictionary as an archaic alternative spelling of the unit of area ARE.