

Zhang's Prime Result Being Improved Everyday - wasd
http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes#World_records

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vishaldpatel
So, what are we looking at here?

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bpicolo
Every prime is within 388,284 numbers of another prime number, effectively, I
believe.

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xerula
No, arbitrarily large gaps between prime numbers exist. But there are no
efficient methods for locating gaps of a particular length. The largest gap
for which the end primes are known, so far, is of length 337,446.

The recent work summarized on the linked page proves something else, namely
that there are infinitely many pairs of prime numbers separated by only
388,284. The goal is to get that number down to two and to prove the twin
prime conjecture. (In your interpretation this would be like saying every
prime is within 2 of another prime, which is obviously false.)

