4 ms·

Does this mean that for any given prime, there will always be a prime within 600 digits? Or that given a set of infinite numbers, you can also construct an infi

• deleted 6y ago
  [deleted]
• ogogmad 6y ago
  > Does this mean that for any given prime, there will always be a prime within 600 digits? No. Euclid showed that the gap between consecutive primes can be arbitrarily large. In particular, n!+2, n!+3, ..., n!+n are all composite whenever n>1. > Or that given a set of infinite numbers, you can also construct an infinite set of pairs of primes 600 digits apart? It means that there are infinitely many pairs of primes p and q such that 0 < |p - q| < 600.
• ColinWright 6y ago
  There are several ways of saying the same thing, and different things resonate with different people. The one I like is this. Go out as far as you like. Somewhere out there ahead of you there are two primes p and q who differ by no more than 600. So there's a prime p with another prime q less than p+600. And now if you start from there and go still further, then you can do it again. No matter how far you will still find primes p and q with p<q<p+600. So there are infinitely many such pairs, because you can always find another one.
• nullc 6y ago
  No, although there is always a prime between x and 2x (for x>3).