It might be worth reminding ourselves that there can be no largest prime number, only (as already noted above) a largest known prime. The implication worth contemplating in this context is that no matter how many gazillion digits a prime number has, it is infinitesimally small (indistinguishable from zero if looked at from far enough away) compared to all the primes that exist.
It is also interesting that, although we have to admit the prime numbers, on average, steadily get further and further apart, there is nevertheless an infinite number of them separated by any given even number, even two. (Primes can't be separated by an odd number since an odd plus another odd number always produces an even number, and even numbers are by definition composite).
Another mind-boggler -- the occurrence of primes in the number sequence seems, by every test we can imagine, to be random, but, of course, it can't be random, as it has to be something determined.
No comments:
Post a Comment