Gapcoin Cryptocurrency: A PeertoPeer Electronic Cash System
Get Gapcoin  Real Crypto  Real Math  Genuine Commodity Money  As Easy as Pi
Useful ProofofWork  Functional Mathematics  Logarithmic Coin Issuance  Unique Blockchain  Distributed Ledger Technology (DLT)
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PRIME GAP OF MAXIMUM KNOWN MERIT  PRESS RELEASE
Q. Now write the expression for the volume of a thick crust pizza with height "a" and radius "z". *

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"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) '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."
"Specifications:
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:
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 : https://faculty.lynchburg.edu/~nicely/
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 (v0.9.24) featuring the above mathematically functional "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 primecounting 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: gapcoin.org
Prime Gap List Project  Prime Gap List Project Resources on GitHub  mersenneforum.org  Prime Gap Search Group
Original Website  gapcoin.org  BitcoinTalk.org 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 original Gapcoin developer John Allen Frey 1991  2017
and Dr. Thomas Nicely 1943  2019 curator of Gapcoin's prime gap records.
Related Reading  Mathematical Resources:
Chinese Remainder Theorem  Functional Mathematics  Mathematical Optimization  Mathematical Constant
Gapcoin Network Status : Strong and Stable
Did you know Gapcoin Club also supports Riecoin ?
Riecoin on Tor v2 Nodes  riecoin.conf
Get Gapcoin  Real Crypto  Real Math  Genuine Commodity Money  As Easy as Pi
Useful ProofofWork  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 Presale  No Premine  No Airdrop  No Chain Forks (yet!)
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