

Infinite number of prime pairs within 70 million of each other - archgoon
https://plus.google.com/117663015413546257905/posts/KR1kyHhYQCA

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robinhouston
It’s a big day for number theory! Harald Helfgott has also proved the odd
Goldbach conjecture, that every odd number greater than five is the sum of
three primes. <http://arxiv.org/abs/1305.2897>

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lysium
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)!

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mappu
I 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

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d0mine
It 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.

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bvaldivielso
I wonder how they got to 70e6, I mean, such a round number.

My guess is that they didn't actually get to that exact number, but a slightly
lower one, more difficult to remember. I don't know though.

