Enigma 1371: Odd big base
19 November 2013
Posted by on
From New Scientist #2530, 17th December 2005
If you want to work in a base higher than 10 you need some new symbols for the higher “digits”. Today I am working in such a base and my “digits” are (in the usual increasing order): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A (= 10), B (= 11), C (= 12), … and so on, using just as many letters of the alphabet as needed.
This means that some numbers look like words. For example, if I were working in base 15 then in my new notation the number BAD would represent the decimal number 2638 (= 11×15² + 10×15 + 13).
I have been looking at some numbers in my new system which do not use any of the traditional digits 0-9, such as ODD, BIG, BASE, NAB and PRIME. In fact more than one of those five numbers is prime.
What is my base?