Chemical and Engineering News recently had an article (locked online) on the iGEM synthetic biology competitions. I wondered if I was young and strong would I be a participant? As part of a rationalization for my never-obsessive life endeavors and consequent lack of creativity, I concluded “no”. Instead I would study (futilely?) the structure of prime numbers. Prime numbers fit no pattern – that is we need to know all the smaller prime numbers to find the next. Counting numbers are the most fundamental numbers we can imagine. Multiplication is a very natural extension of addition and yet some numbers are prime (can’t be factored) and some are not (composite) and there is no rule to tell which is which. To find if a number is prime the best we do is try to form a rectangle with that number of dots.
So maybe counting numbers are not fundamental. Maybe there is another number structure wherein prime numbers emerge naturally – some dark matter mathematical structure that holds everything together.