https://github.com/h5law/primality

A Go library for checking whether an integer is prime or not, using either the AKS or Miller-Rabin algorithms.
https://github.com/h5law/primality

aks go golang miller-rabin number-theory primality-test prime-numbers

Last synced: about 2 months ago
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A Go library for checking whether an integer is prime or not, using either the AKS or Miller-Rabin algorithms.

• Host: GitHub
• URL: https://github.com/h5law/primality
• Owner: h5law
• License: bsd-3-clause
• Created: 2024-05-17T02:14:27.000Z (over 1 year ago)
• Default Branch: main
• Last Pushed: 2024-05-22T11:37:30.000Z (over 1 year ago)
• Last Synced: 2025-03-17T12:41:56.274Z (7 months ago)
• Topics: aks, go, golang, miller-rabin, number-theory, primality-test, prime-numbers
• Language: Go
• Homepage: https://pkg.go.dev/github.com/h5law/primality
• Size: 36.1 KB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# primality

Primality is a Golang library for determining whether any given integer

$i\in\mathbb{Z}^+,~i\ge1$. The library provides two implementations of algorithms

for determining the primality of an arbitrarily sized integer, using the `math/big`

library.

The two methods provided are the Miller-Rabin and AKS primality test the former

being probabilistic and the latter deterministic, meaning that the Miller-Rabin

primality test doesn't guarantee 100% accuracy in certain situations. Whereas

the AKS primality test is always 100% accurate - but a lot slower on larger

integers.

## Features

### Miller-Rabin:

- Highly accurate probabilistic primality test

  - 25 rounds and force usage of base 2 recommended for near 100% accuracy

- Arbitrarily large integer support (`big.Int`)

- $\mathcal{O}(r\cdot s)$ time complexity (assuming `big.Int` operations are

  $\mathcal{O}(1)$ where $r$ is the number of repetitions and $s$ the number of

  trailing zeros on $n$, the number being tested - otherwise it is related to

  the operations of `big.Int` integers and $n$ itself.

  - As a prime must be odd $s\le7$ meaning the time complexity in its worst case

    is $\mathcal{O}(175)=\mathcal{O}(1)$ with 25 repetitions.

### AKS

- Deterministic primality test

  - Slow overall - but guarantees 100% a valid outcome

- `int` support only

## TODOs

- Improve speed of the AKS method

  - Specifically step 5 but overall it is slow

- Make the AKS method work on arbitrarily sized integers

  - use `big.Int`s over `int`s

- Determine the true time and space complexities for both methods