＠sigma-js/primes

@sigma-js/primes is a javascript library that enables fast detection of prime numbers and prime number arithmetic with the following characteristics.

• The default setting uses the Sieve of Eratosthenes to generate a list of prime numbers ranging from 1 to 8388607.
• The generated prime number list is used for prime number detection and prime number arithmetic, allowing for high-speed processing.
• However, if the target prime number is larger than the default setting, the processing time for generating prime numbers may become longer. In this case, the range of prime numbers to be generated can be narrowed down or an appropriate algorithm (Eratosthenes sieve or Atkin sieve) can be set according to the range of prime numbers to speed up the process of prime number generation even for large numbers.

Install

Install with npm:

1$ npm i @sigma-js/primes

Usage

JavaScript require

1const { isPrime, isCoprime, getPrimes … } = require("@sigma-js/primes");

TypeScript import

1import { isPrime, isCoprime, getPrimes … } from "@sigma-js/primes";

Call example: init

1// You can default settings can be changed
2init({ sieveType: "atkin" }); // default: { sieveType: "eratosthenes" } -> after setting: { sieveType: "atkin" }
3init({ minNum: 1234567 }); // default: { minNum: 1 } -> after setting: { minNum: 1234567 }
4init({ maxNum: 8901234 }); // default: { maxNum: 8388607 } -> after setting: { maxNum: 8901234 }
5init({ sieveType: "atkin", minNum: 1234567, maxNum: 8901234 }); // set all at once

Call example: isPrime

1// You can get the result if the specified number is prime.
2isPrime(3); // Output: true
3isPrime(8); // Output: false
4isPrime(8388607); // Output: false

Call example: isCoprime

1// You can get the result if the given numbers are coprime.
2isCoprime(15, 28); // Output: true
3isCoprime(8, 12); // Output: false

Call example: getPrimes

1// You can specify a range and get the prime numbers in that range.
2init({ minNum: 100, maxNum: 150 }); // Set maximum value to 100 and maximum value to 150
3getPrimes(); // Range: 100～150, Output: [101, 103, 107, 109, 113, 127, 131, 137, 139, 149]
4getPrimes(125); // Range: 125～150, Output: [127, 131, 137, 139, 149]
5getPrimes(110, 140); // Range: 110～140, Output: [113, 127, 131, 137, 139]

Call example: getPrimesAverage

1// You can get the average of prime numbers within a specified range.
2init({ maxNum: 30 }); // Set the maximum value to 30
3getPrimesAverage(); // Range: 1～30, Rounded to third decimal places, Output: 12.9
4getPrimesAverage(25); // Range: 25～30, Rounded to third decimal places, Output: 29
5getPrimesAverage(5, 30); // Range: 5～30, Rounded to third decimal places, Output: 15.5
6getPrimesAverage(1, 5, 9); // Range: 1～5, Rounded to the ninth decimal place, Output: 3.333333333
7getPrimesAverage(5, 12, 9); // Range: 5～12, Rounded to the ninth decimal place, Output: 7.666666667
8getPrimesAverage(5, 12, 0); // Range: 5～12, Rounded to the first decimal place, Output: 8

Call example: getPrimesCount

1// You can get the number of prime numbers in a specified range.
2init({ maxNum: 20 }); // Set the maximum value to 20
3getPrimesCount(); // Range: 1～20, Output: 8
4getPrimesCount(6); // Range: 6～20, Output: 5
5getPrimesCount(1, 10); // Range: 1～10, Output: 4

Call example: getPrimesIndex

1// You can get the correct index of prime numbers in a given range.
2init({ maxNum: 25 }); // Set the maximum value to 25
3getPrimesIndex(3); // Range: 1～25, Output: 2
4getPrimesIndex(17, 10); // Range: 10～25, Output: 3
5getPrimesIndex(2, 1, 10); // Range: 1～10, Output: 1

Call example: getPrimesMedian

1// You can get the number of prime numbers in a specified range.
2init({ maxNum: 100 }); // Set the maximum value to 100
3getPrimesMedian(); // Range: 1～100, Output: 41
4getPrimesMedian(25); // Range: 25～100, Output: 60
5getPrimesMedian(5, 34); // Range: 5～34, Output: 17
6getPrimesMedian(5, 50); // Range: 5～50, Output: 23

Call example: getPrimesSum

1// You can get the sum of prime numbers within a specified range.
2init({ maxNum: 30 }); // Set the maximum value to 30
3getPrimesSum(); // Range: 1～30, Output: 129
4getPrimesSum(25); // Range: 25～30, Output: 29
5getPrimesSum(5, 30); // Range: 5～30, Output: 124

Call example: getPrimesTwins

1// You can get twin prime numbers within a specified range.
2init({ maxNum: 20 }); // Set the maximum value to 20
3getPrimesTwins(); // Range: 1～20, Output: [[3, 5],[5, 7],[11, 13],[17, 19]]
4getPrimesTwins(6); // Range: 6～20, Output: [[11, 13],[17, 19]]
5getPrimesTwins(1, 10); // Range: 1～10, Output: [[3, 5],[5, 7]]
6getPrimesTwins(3, 4); // Range: 3～4, Output: []

Call example: getFactors

1// You can obtain the prime factorization result of the specified number.
2getFactors(24); // Output: [2, 2, 2, 3]
3getFactors(555); // Output: [3, 5, 37]

Call example: getFactorsFormula

1// You can get the prime factorization result of the specified number using a formula.
2getFactorsFormula(24); // Output: "2^3*3"
3getFactorsFormula(30); // Output: "2*3*5"
4getFactorsFormula(7); // Output: "7"

Call example: getMultInverse

1// You can get the multiplicative inverse of a given number.
2getMultInverse(3, 11); // Output: 4 (Get x that becomes 3*x≡1(mod 11))
3getMultInverse(7, 13); // Output: 2 (Get x that becomes 7*x≡1(mod 13))

Call example: getRandomPrime

1// You can get prime numbers randomly within a specified range.
2init({ maxNum: 100 }); // Set the maximum value to 100
3getRandomPrime(); // Range: 1～100, Output: 7
4getRandomPrime(10); // Range: 10～100, Output: 11
5getRandomPrime(4, 12); // Range: 4～12, Output: 5

License

Copyright (c) 2023, s-hama. Released under the MIT License.

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