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

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Useful Proof of Work | Functional Mathematics | Logarithmic Coin Issuance | Unique Blockchain

... The largest decentralized prime gap search + new world record attempt commencing from 21st Oct. 2018 - Join us! ...


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


New Re-launch: GAP Exchange / BTC Market at Nova Exchange (Trading Commences Dec. 3rd 2018)

Buy GAP with Credit or Debit Card at Indacoin | GAP Exchange / BTC Market at Cryptopia (on hold until Jan. 10th 2019)

Real CPU mining on your own PC or try Cloud Mining Gapcoin today! | Gapcoin on Tor Nodes

Download the Gapcoin Wallet:

  • MS Windows (64-bit) v0.9.2 - gapcoin-qt.exe or gapcoin-qt.exe - md5: f81557f61ee14dc1d1ded244f9064dad
  • Easy in-wallet Windows mining guide | gapcoin.conf - Non-Tor Version

  • Linux v0.9.2 - or - md5: 50551e97df7cdfd672a66ebf059cee20
  • Gapcoind server or desktop set-up | gapcoin.conf - Non-Tor Version

  • Source Code - - md5: 02113c4253c5fa50fdb5d8d6fc6ae523
  • Download Resources -
  • Original Github -
  • What is Gapcoin?

    Gapcoin is a prime number based p2p cryptocurrency, which eliminates the sticking points of other scientific currencies like Primecoin or Riecoin. It's a 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 (with fast confirmations like Litecoin = 4x faster transactions than the Bitcoin or Bitcoin Cash networks!)
  • 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)
  • 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 lager 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 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 41.94, every block will be a new world record!

    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. 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)

    Source: 'Official' Gapcoin website:

    Visit the Official Website - | Forum Announcement | Gapcoin Source Code | Gapcoin Block Explorer

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

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    Get Gapcoin | Real Crypto | Real Math | Genuine Commodity Money

    Useful Proof of Work | Functional Mathematics | Logarithmic Coin Issuance | Unique Blockchain

    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 Chain Forks (yet!) - - content copyleft 2018 - 2019

    Software © MIT License. No Rights Reserved.