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Old 2016-01-17, 15:35   #1
robert44444uk
 
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Jun 2003
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Default Welcome to the Prime Gaps Search Forum

Welcome to the prime gap search forum.

The purpose of the forum is to act as a discussion area and an information exchange for those people interested in prime gaps.

We have a number of active searches going on, but all of the searches have something in common, the search for candidates that qualify to be listed on Dr Thomas Nicely’s website

http://www.trnicely.net/gaps/gaplist.html

The Nicely site keeps records of gaps of a specified length between two integers that are proven prime or shown to be probable primes. Each integer between the two end points is proven to be composite.

This forum is particularly interested in prime gaps that have a merit of great than 10. For a given prime p, the average prime gap to the next prime is given by ln(p), where ln is the natural logarithm. The merit of a gap g is given by g/ln(p).

There is little point in looking for gaps <1,352 as an exhaustive search of primes up to 4*10^18 has been carried out and all gaps smaller than this have been found.

As of the summer of 2014, the Nicely site had early instance prime gaps with merit >10 listed for all possible gaps <60,000 and an early effort by this forum has been to extend the early instance list up to 100,000.

At the far end of the scale, the forum is helping to support the largest gap search, looking at a candidate gap (4,680,156) provide by mart_r. This has a merit >20.

The forum also is looking at new approaches for finding large merit gaps. For example, a theoretical approach that looks at the modular relations of small primes over a range of 2310 integers that might provide record gaps in the range 1,350-4,000.

Last, but not least, the forum looks to develop gap hunting programs that can help to find those large merit gaps.

Last fiddled with by robert44444uk on 2016-01-17 at 15:39
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Old 2018-06-03, 01:54   #2
Bobby Jacobs
 
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This forum is great. Thank you for creating the prime gap searches.
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Old 2019-09-23, 01:00   #3
rudy235
 
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Default Predicting Maximal Gaps in Sets of Primes

https://arxiv.org/pdf/1901.03785.pdf . This Paper was published recently on May 22nd 2019

There is a reference (3) to the Search reaching 264

Article
Predicting Maximal Gaps in Sets of Primes
Alexei Kourbatov1 and Marek Wolf

[…]
References
.
3. Nicely, T.R. First Occurrence Prime Gaps, Preprint. 2018. http://www.trnicely.net/gaps/gaplist.html
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