Gapcoin Cryptocurrency: A Peer-to-Peer Electronic Cash System

Get Gapcoin | Real Crypto | Real Math | Genuine Commodity Money | As Easy as Pi

Useful Proof-of-Work | Functional Mathematics | Logarithmic Coin Issuance | Unique Blockchain | Distributed Ledger Technology (DLT)

... The largest decentralized prime gap search + new world record and attempt ongoing! - Join us! ...


Q. Now write the expression for the volume of a thick crust pizza with height "a" and radius "z". *

NEW: Gapcoin Project Community Website


GAP Exchange / BTC Markets at:

FreiExchange (Live!), FreeBitcoins XChange (Live! Recommended!) and C-PatEx (Live!)

Gapcoin Swap XChange (Live!) and Gapcoin Faucet (Live!)

Unnamed Exchange (Live!) and Vote for Gapcoin at SouthXchange

Caveat emptor "buyer beware" BSV and BCH are NOT original Bitcoin. Bitcoin is BTC

GAP Exchange / LTC Markets at: Unnamed Exchange (Live!) and C-PatEx (Live!)


Gapcoin Mining Pool:

Mine Gapcoin's in-wallet on your own PC and/or with a full-node / Cloud Server instance!

Download the latest v0.16.3 Gapcoin Wallet:


  • N.B. If you are running the old v0.9.x release - You are advised to BACKUP your wallet and EXPORT your private keys before upgrading.

  • Old Source Code - - md5: 02113c4253c5fa50fdb5d8d6fc6ae523
  • Original Github (old) -
  • Mining Pool Source Code (old) + Stratum -

  • "What is Gapcoin?

    Gapcoin is a prime number based P2P cryptocurrency, which eliminates some sticking points of other scientific currencies like Primecoin or Riecoin. It's a (code, not chain) 'fork' of Satoshi Nakamoto's Bitcoin, a decentralized payment system which is independent of banks, governments and other centralized regulators. With Gapcoin, you can send money around the globe in seconds. The big improvement in comparison to Bitcoin is that instead of burning electricity for it's own sake, Gapcoins Proof of Work function actually does useful work by searching for large prime gaps."


  • PoW: custom, prime gaps
  • Block target time 2.5 minutes (fast confirmations like Litecoin = 4x faster transaction confirmations than Bitcoin! **)
  • Block reward proportional to the current difficulty
  • Block reward halving every 420000 (about 2 years)
  • Cap: about 10 - 30 million GAP
  • Difficulty adjusts every block and increases logarithmically (it will probably take years to get to 50)"

  • ** based on the 10 minute average block time (Bitcoin) vs 2.5 minute average block time (Gapcoin).
  • Logarithmic Spiral Pylab.svg
    By Morn the Gorn - Own work, Public Domain, Link

    "Fair launch:

    Gapcoin was not designed to enrich the early adopters or the coin creators! Unlike Primecoin, the more people that mine Gapcoin, the more coins per block will be produced. (Coin supply will increase logarithmically with the difficulty, this means it will grow in the beginning, but later, it won't change that much.)

    There wasn't any premine!

    To avoid instamine, the reward of the first 1152 blocks (about 48 hours) increased quadratically to it's absolute value: the current difficulty. The block reward was 1/1152^2 * blockheight^2 * difficulty for the first 1152 blocks. The source code was made available before launch (excluding the PoW function), so that everyone could setup their own testing environment, compile the software, and check that everything works. Windows and Linux binaries were distributed in an encrypted container before launch, the password was revealed at launch on Tue Oct. 21 2014 - 18:00:00 UTC"

    "How is Proof of Work actually designed?

    A PoW algorithm has to fit two specifications:

  • It must be cryptographically secure (a PoW must not be reusable)
  • It must be hard to calculate, but easy to verify
  • Verifying a prime gap is easy, you only have to check every number between the start and the end to be composite. Calculating is harder, much harder! Large prime gaps occur a lot lesser than smaller ones. According to E. Westzynthius, in e^n prime gaps there will be one gap that is n times greater than the average prime gap."

    "So the difficulty will simply be the length of the prime gap?

    Not exactly. The average length of a prime gap with the starting prime p, is log(p), which means that the average prime gap size increases with larger primes. Then, instead of the pure length, we use the merit of the prime gap, which is the ratio of the gap's size to the average gap size.

    Let p be the prime starting a prime gap, then m = gapsize/log(p) will be the merit of this prime gap.

    Also a pseudo random number is calculated from p to provide finer difficulty adjustment.

    Let rand(p) be a pseudo random function with 0 less than rand(p) less than 1. Then, for a prime gap starting at prime p with size s, the difficulty will be s/log(p) + 2/log(p) * rand(p), where 2/log(p) is the average distance between a gap of size s and s + 2 (the next greater gap) in the proximity of p.

    When it actually comes to mining, there are two additional fields added to the Blockheader, named “shift” and “adder”. We will calculate the prime p as sha256(Blockheader) * 2^shift + adder. As an additional criterion the adder has to be smaller than 2^shift to avoid that the PoW could be reused."

    "Could we break any world records?

    In 2017 (confirmed in early 2018) the Gapcoin network found a new prime gap of maximum known merit! 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. Source :

    We already broke more than 544 records of first known occurrence prime gaps. (Note: New record data to be updated from the blockchain).

    Also, if the difficulty reaches (or spikes above) 41.94, every block will be a new world record!"

    Gapcoin's highest found merits as of 10th September 2019 (Top 30)

  • -
  • -
  • Does Gapcoin have a Whitepaper?

    The original developer did not produce a whitepaper for Gapcoin.

    We recommend that you read the original Bitcoin whitepaper and realize that Gapcoin is effectively Bitcoin featuring the above mathematically functional proof-of-work "bells and whistles" optimizations.

    "But how are prime gaps useful?

    Prime numbers are interesting for lots of mathematicians around the globe, and they're also important to every day cryptography (see RSA).

    Researches about prime gaps could not only lead to new breakthroughs in the bounded gap, it may also help proving the Twin Prime Conjecture and maybe even the millennium problem, the Riemann hypothesis. Who knows?"

    "Last but not least, what does the original Gapcoin logo have to do with prime gaps?

    The formula π(x) is known as the prime-counting function, the graph shows the prime gap distribution as well. That's why the “π” fits the logo perfectly. (image Wikipedia)"

    The latest Gapcoin logo is based on a Logarithmic Spiral and Pizza Pi, of course!

    Source: "The Original" Gapcoin website:

    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

    * A. The formula for volume is π·(radius)2·(height). In this case, pi·z·z·a !

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

    Related Reading - Mathematical Resources:

    Large gaps between consecutive prime numbers - Kevin Ford, Ben Green, Sergei Konyagin, Terence Tao

    Long gaps between primes - Kevin Ford, Ben Green, Sergei Konyagin, James Maynard, Terence Tao

    Together and Alone, Closing the Prime Gap | After Prime Proof, an Unlikely Star Rises

    Prime Gap Grows After Decades-Long Lull | Unheralded Mathematician Bridges the Prime Gap

    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

    Other Cool Prime Gap Related Software, Tools and Projects:

    Prime Gap Searching

    List of known first occurrence prime gaps

    Server to validate and colate prime gap records

    Tool to verify large prime gaps

    Related Wiki Links:

    Pi | Prime Numbers | Prime Gaps | Fibonacci Number | Fibonacci Cube

    Chinese Remainder Theorem | Functional Mathematics | Mathematical Optimization | Mathematical Constant

    Complex Logarithm | Natural Logarithm | Irrational Number | Golden Ratio | Helix

    Gapcoin Network Status : Strong and Stable

    Did you know Gapcoin Club also supports Riecoin ?

    Disclaimer(s) (Warning): Gapcoin (GAP) is NOT associated with the gapschain AI token project (GAPS)

    Gapcoin (GAP) is NOT associated with the "Pi Network" project.

    Get Gapcoin | Real Crypto | Real Math | Genuine Commodity Money | As Easy as Pi

    Useful Proof-of-Work | Functional Mathematics | Logarithmic Coin Issuance | Unique Blockchain | Distributed Ledger Technology (DLT)

    Original "Bitcoin" Technology Since 2014 | Not a Financial Product or Service | Cryptocurrency as "Sound Money" and Digital Cash

    Not a Token | Not an ICO | No Pre-sale | No Pre-mine | No Air-drop | No Chain Forks (yet!)

    Free (Libre) and Open Source Software ... developers required ... v0.16.3 content Copyleft 2018 - 2022

    Software MIT License. No Rights Reserved.