Gapcoin Cryptocurrency - New Prime Gap of Maximum Known Merit


Source :


" The Gapcoin network (Jonnie Frey, developer), a Bitcoin derivative which employs a hashing algorithm to search for prime gaps of high merit, has discovered a new prime gap of maximum known merit, a gap of G=8350 following the 87-digit prime P1=293703234068022590158723766104419463425709075574811762098588798217895728858676728143227. The merit M=G/ln(P1) of this gap is M=41.93878373153988, the largest merit of any known prime gap, and the first prime gap to be discovered with a merit exceeding 40. The endpoints of the gap have been certified as primes deterministically, using the Akiyama-Kida-O'Hara UBASIC implementation (1988-1992) of the APRCL2 test, due to Adleman, Pomerance, Rumely, Cohen, H. W. Lenstra, and A. K. Lenstra (1984-1987).

However, Bertil Nyman's maximal gap of 1132, following the prime 1693182318746371 (discovered 24 January 1999), continues to exhibit the greatest known value (0.92063858855742) of the Cramér-Shanks-Granville ratio G/ln²(p_1); this ratio is 0.210642105494715467 for the new Gapcoin gap. The limit superior of this ratio has been conjectured to be unity (or some even larger value); see the discussion in "New prime gaps between 1e15 and 5e16".

Thanks to Dana Jacobsen for alerting me to the discovery of this gap. "

gapcoin world record prime gap 2017 wikipedia

Screenshot from wikipedia :


Original Developer (account) Statement via : forum

Gapcoin Club Contact : gapcoin-core (at) protonmail (dot) com

Gapcoin Media References:

Times of Malta - Prime numbers and cryptography - 10 March 2018

Research Papers Referencing Gapcoin's Results:

Combined Sieve Algorithm for Prime Gaps 11/30/2020 by Seth Troisi, et al.

On the nth Record Gap Between Primes in an Arithmetic Progression 2018 by Alexei Kourbatov

Prime Gap List Project:

Top 20 overall merits | Exhaustively analyzed gaps

Recovery and curation of Dr. Thomas Ray Nicely’s list of first known occurrence prime gaps

Prime Gap List Project | Prime Gap List Project Resources on GitHub | - Prime Gap Search Group

Original Website - | Old Forum Announcement | Old Gapcoin Source Code | Gapcoin Block Explorer

In memory of Dr. Thomas Nicely 1943 - 2019 curator of Gapcoin's prime gap records.

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