Primes distribution as creativity pattern

When researching on some complicated issue for transforming Word files into PDF format programmatically, I came across an interesting website: Project Euler. That site offers numerous mathematical problems for solving by means of computer programming. Many of them are about miscellaneous properties of prime numbers.

Leonard Euler was a Swiss mathematician who worked most of his scientific life in Russia. He has contributed a lot to mathematics and anybody who learned math somehow in the past would be able to recollect a thing or two related to that renown scientist. There are many discoveries made by him in the field of prime numbers as well.

Prime numbers is one of the most incomprehensible concepts in arithmetics. It defies intuition and, is a way, common sense too. Paul Erdos, probably most eccentric mathematician of all times, spent many years researching the topic and was so baffled by primes properties that he re-phrased Eistein's expression - maybe God does not roll dice in the Universe but something really strange is going on with prime numbers.

Best known property of primes is probably that there is infinite number of them among integers. The proof of that fact is a classic example of the approach called Reductio ad absurdum. This is when you pretend that there is a greatest prime number somewhere far away and disproving that by the ability to construct even greater prime. Another property is that there are primes separated by just one integer, like 3 and 5, or 41 and 43. They are referred to as twin primes. One of the biggest mysteries in math is whether or not there is an infinite number of those twin pairs.

But one particular attribute of primes plunges me into abyss of ultimate mental discomfort each time I think of it. It is distribution of them among other integers. It is proven logically, mathematically, beyond any doubt, that there are intervals of consecutive integers of any imaginable length that do not contain any primes. You can pick some unknown (but existent!) integer N and surely there is no primes between N and (N + 1000). Or N and (N + 1000000). An so on.

That curious feature led me to a weird analogy. Creativity as a process (at least as I am familiar with it) is highly irregular. Primes distribution is a good way to describe it - there can be extremely long periods with not even a hint for any creativity spark, almost endless intervals of mental drought. Then something comes up and I am able to accomplish a little bit, not necessarily terribly significant. Does infinity of primes can be anyhow hopeful consideration in that regard? Yes and no, as professional database administrators and software consultants love to say. Yes, because there is always a chance that any given fruitless period will end. No, because days of human life are very much limited by its nature unlike number of primes among integers. Despite those long primeless stretches, primes do have important ally on their side - infinity.