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The aim is to establish a bound on the gaps between consecutive prime numbers.

February 20, 2014Annals of MathematicsOpen Access

Bounded gaps between primes

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The aim is to establish a bound on the gaps between consecutive prime numbers.
Proving the lim inf of the gaps between consecutive primes (pn+1 - pn) is less than 7 x 10^7.
Utilizing mathematical techniques from number theory to derive the inequality.
The established limit is lim inf n (pn+1 - pn) < 7 x 10^7, indicating bounded gaps between consecutive primes.

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Mathematical proof shows that gaps between consecutive primes are bounded, indicating deep number theory insights.

It is proved that lim inf n (pn+1 -pn) < 7 10 7 , where pn is the n-th prime.

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Zhang Yitang (2014) studied this question.

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Mathematical proof shows that gaps between consecutive primes are bounded, indicating deep number theory insights.

It is proved that lim inf n (pn+1 -pn) < 7 10 7 , where pn is the n-th prime.