akgupta89 / prime-multiplication-table

Node.JS/ES6 implementation of a prime multiplication table

Prime Multiplication Table

JavaScript implementation of a prime multiplication table generator.

Overview

Create a program that generates a multiplication table of N primes and output it to Command Line. The first row and first column will show a list of prime numbers.

Solution

This program uses a variation of the 2-3-5-7 wheel sieve generator to generate prime numbers using a generator function. The base algorithm is a modification of the a prime number generator snipped provided by Vladimir Agafonkin.

Complexity

Time Complexity

• The prime number generator algorithm has a time complexity of O(n).
• The prime multiplication table has a time complexity of O(n^2). Optimization is done by mirroring the multiplication table above the top-left to bottom-right diagonal axis, cutting computation time approximately in half.

Space Complexity

• The prime number generator algorithm has a space complexity of O(sqrt(n)).
• The prime multiplication table has a space complexity of O(n^2)

How does it scale?

The generator can generate a million prime numbers in under a second on a modern computer, and keep returning prime numbers consecutively, allowing the program to theoretically scale infinitely.

Install

1. Clone the repo, make sure you have Node.JS installed
2. Run npm install
3. Run node main.js 10
4. Change the number 10 to any positive integer

Testing

1. Run npm test

License

MIT