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On the one hand there's all these reports of the largest prime gap between all numbers proven to be < 246. On the other hand, I read reports of ...

In the following table we list the maximal gaps through 1355. These are the first occurrences of gaps of at least this length . For example, there is a gap of 879 composites after the prime 277900416100927. This is the first occurrence of a gap of this length, but still is not a maximal gap since 905 composites follow the smaller prime

Usually the ratio of gn / ln(pn) is called the merit of the gap gn . As of September 2017 , the largest known prime gap with identified probable prime gap ends has length 6582144, with 216841-digit probable primes found by Martin Raab. This gap has merit M = 13.1829. The largest known prime gap with identified proven primes as gap ends has length 1113106 and merit 25.90, with 18662-digit primes found by P. Cami, M. Jansen and J. K. Andersen.

The largest gap between successive prime numbers is unbounded. The larger the prime number, the larger the average gap between it and its successor or ...

15.12.2021 · OEIS: A077800. As a result, the sum of any pair of twin primes (other than 3 and 5) is divisible by 12. Are prime gaps bounded? In other words, that the gap between one prime and the next is bounded by 70,000,000 infinitely often—thus, the “bounded gaps” conjecture. On first glance, this might seem a miraculous phenomenon.

Quick Answer: What Is The Largest Gap Between Primes? Contents As of August 2018 the largest known maximal prime gap has length 1550, found by Bertil Nyman. It is the 80th maximal gap, and it occurs after the prime 18361375334787046697. Why 2 and 3 are the only consecutive prime numbers?

Large gaps between primes Pages 915-933 from Volume 183 (2016), Issue 3 by James Maynard Abstract We show that there exist pairs of consecutive primes less than x whose difference is larger than t ( 1 + o ( 1)) ( log x) ( log log x) ( log log log log x) ( log log log x) − 2 for any fixed t. This answers a well-known question of Erdős.

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If p is a prime, the 'prime gap' after p is the number of composites that follow it. maximal gaps are larger than those for any smaller primes p.

05.02.2015 · I find consistently conflicting information online. On the one hand there's all these reports of the largest prime gap between all numbers proven to be < 246. On the other hand, I read reports of the largest known prime number gap being 1476.

19.04.2016 · Large gaps between consecutive prime numbers Pages 935-974 from Volume 183 (2016), Issue 3 by Kevin Ford, Ben Green, Sergei Konyagin, Terence Tao Abstract Let G ( X) denote the size of the largest gap between consecutive primes below X. Answering a question of Erdős, we show that G ( X) ≥ f ( X) log X log log X log log log log X ( log log log X) 2,

Therefore, the difference between two successive primes p_k and p_(k+1) bounding a ... is the length of the largest prime gap that begins with a prime p_k ...

Large gaps between primes Pages 915-933 from Volume 183 (2016), Issue 3 by James Maynard Abstract We show that there exist pairs of consecutive primes less than x whose difference is larger than t ( 1 + o ( 1)) ( log x) ( log log x) ( log log log log x) ( log log log x) − 2 for any fixed t. This answers a well-known question of Erdős.

As of September 2017, the largest known prime gap with identified probable prime gap ends has length 6582144, with 216841-digit probable primes found by ...

Dec 07, 2015 · However, when we're looking for "good" primes we can thin the herd even more. If gcd (x, 60) = 1, we find that in most cases gcd (x-1, 60) is either 6 or 10. There are 6 values of x for which it is 2: 17, 23, 29, 47, 53, 59. Therefore we can precompute the "good" primes of the form 2^a 3^b + 1 and 2^a 5^b + 1 and merge them into the result of a ...

In the following table we list the maximal gaps through 1355. These are the first occurrences of gaps of at least this length . For example, there is a gap of 879 composites after the prime 277900416100927. This is the first occurrence of a gap of this length, but still is not a maximal gap since 905 composites follow the smaller prime