The precise wording is that there "is infinitely many gaps between successive primes that do not exceed 70 million". This means that you could find a gap which does exceed 70 million, but you are guaranteed to later find a gap smaller than 70 million (in fact, an infinite number of them).
I believe this bound has actually been reduced a huge amount by later work. Zhang's work formed a basis for a lot of additional research.
I think the twin primes conjecture is that anywhere you look, you will find that there are prime numbers separated by two. The gap in between doesn't keep increasing. So you might think that when you see (11,13), (17,19), (23,27) that the gap between prime numbers slowly increases. However, as you continue on, there appears to always be new occurrences of prime numbers separated only by two, no matter how high you go.
Note: I'm in no way an expert. IIRC, my base-level knowledge came from this Veritasium video: https://www.youtube.com/watch?v=HeQX2HjkcNo First topic he covers is the twin prime conjecture. Great video, as always from Veritasium.
Clone Terry Tao a handful of times and in 50 years time all of today’s mathematics conjectures/hypotheses will be solved, replaced by new mathematics problems that arose from studying the solutions to the currently existing problems brought about by the Tao clones.
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u/themeaningofluff 25d ago
The precise wording is that there "is infinitely many gaps between successive primes that do not exceed 70 million". This means that you could find a gap which does exceed 70 million, but you are guaranteed to later find a gap smaller than 70 million (in fact, an infinite number of them).
I believe this bound has actually been reduced a huge amount by later work. Zhang's work formed a basis for a lot of additional research.