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If that holds, that's huge! It means, the distance between consecutive prime numbers does not grow unbounded (but is bounded by at least 70e6)!
by lysium 13y ago
If that holds, that's huge! It means, the distance between consecutive prime numbers does not grow unbounded (but is bounded by at least 70e6)!
- ColinWright 13y agoYou are mistaken - gaps between prime grow unboundedly large - it's a common first year exercise in number theory to show that.
- tzs 13y agoWell, he's mistaken if what he is saying is what you think he is saying, but I think his statement is ambiguous. I think he might mean when he says the gap does not grow unbounded is that that you never reach a point where the gaps are ALL arbitrarily large. As we run through the primes, we'll always continue to find gaps that are 70 million or less.
- lysium 13y agoYou are both correct! ;-)
- mappu 13y agoI think you're making a stronger statement than the article - it's certainly possible for there to be an infinitely many pairs of primes less than 70e6 apart, without there being another prime within 70e6 either side of a given prime number
- d0mine 13y agoIt is especially obvious given that the goal is to lower the boundary from 70e6 to 3. There are i such that |prime[i] - prime[i+1]| >= 3 but it doesn't prevent the possibility that there are infinite number of pairs such that |p - q| < 3 where p, q are primes.