Mar 18, 2021 • Jonny Frey, edited by Graham Higgins • ~ 4 min to read • gapminer

```
GapMiner Copyright (C) 2014 The Gapcoin developers <info@gapcoin.org>
Required Options:
-o --host host ip address
-p --port port to connect to
-u --user user for gapcoin rpc authentification
-x --pwd password for gapcoin rpc authentification
Additional Options:
-q --quiet be quiet (only prints shares)
-e --extra-verbose additional verbose output
-j --stats-interval interval (sec) to print mining informations (default 10)
-t --threads number of mining threads
-l --pull-interval seconds to wait between getwork request
-m --timeout seconds to wait for server to respond
-c --stratum use stratum protocol for connection
-s --sieve-size the prime sieve size (default 33554432)
-i --sieve-primes number of primes for sieving (default 900000)
-f --shift the adder shift (default 25)
-r --crt use the given Chinese Remainder Theorem file
-d --fermat-threads number of fermat threads wen using the crt
--calc-ctr calculate a chinese remainder theorem file
--ctr-strength more = longer time and mybe better result
--ctr-primes the number of to use primes in the ctr file
--ctr-evolution whether to use evolutional algorithm
--ctr-fixed the number of fixed starting prime offsets
--ctr-ivs the number of individuals used in the evolution
--ctr-range percent deviation from the number of primes
--ctr-bits additional bits added to the primorial
--ctr-merit the target merit
--ctr-file the target ctr file
-h --help print this information
-v --license show license of this program
```

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.

Instead of the pure length, Gapcoin uses the “merit” of a prime gap which is the ratio of the gap’s size to the average gap size. If $p$ is the prime starting a prime gap then $m\; =\; gapsize/log(p)$ will be the *merit* of this prime gap.

A pseudo-random number is calculated from $p$ to provide finer difficulty adjustment. Let $rand(p)$ be a pseudo-random function with $0\; <\; rand(p)\; <\; 1$.

Then, for a prime gap starting at prime $p$ with size $s$, the difficulty will be $s/log(p)\; +\; 2/log(p)\; \ast \; rand(p)$ 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 block header, named “shift” and “adder”.

We will calculate the prime $p$ as `sha256(block header) ∗ 2^shift + adder`

.

As an additional criterion, the adder has to be smaller than $2^shift$ to avoid a situation in which the PoW could be reused.

Calculate the first $n$ primes. In the actual sieve we skip all even numbers because we want to only sieve the odd multiplies of each prime.

So, we create an additional set of primes and multiply each with two. Make sure the `start_index`

of the sieve is divisible by two.

Now calculate for each prime the first odd number in the sieve which is divisible by that prime (called `pindex`

).

For each prime $p$: mark `pindex`

as composite, add $2\; \ast \; p$ to `pindex`

and mark it as composite, redo till we reach the end of the sieve.

For each remaining prime candidate, check primality with the Fermat-pseudo-prime-test as it is faster than the Miller-Rabin-test (Fermat is not as accurate as the Miller-Rabin and maybe some valid sieve results will not be accepted but this should be very rare)

Now scan the remaining (pseudo) primes for a big prime gap.

We do not check every remaining prime candidate with the Fermat test. Instead we look how large the gap has to be to fit the required difficulty (`max_length`

).

Then we determine the first prime in the sieve (called `pstart`

). Now we scan the prime candidates in the range `(pstart, pstart + max_length)`

. We start at the position `(pstart + max_length)`

and scan every prime candidate in reverse order till we reach `pstart`

.

If we find a prime within the range `(pstart, pstart + max_length)`

we can skip all other prime candidates within that range and set `pstart`

to that prime.

We redo the above process till we reach the end of the sieve.

`start_index`

can be `hash ∗ 2^shift + [0, 2^shift]`

*( start_index no longer appears in the source code)*

The maximum sieve size ~~depends on ~~ is defined in the source code as the maximum capacity of a `start_index`

and is limited by `(hash + 2^shift) - start_index`

`long long int`

(9223372036854775807), the default is specified to be 33554432.

The shift can theoretically be in the range `[14, 2^16]`

but nodes can choose to only accept shifts up to a given amount (e.g. 1024 for the main nodes)

Copyright © 2021, Gapcoin Project.