johsteffens / qprimes

Prime Number Generator - Quick and Simple - 64 Bit Numeric Range

Fast and Simple 64-bit Prime Generator

What it is

qprimes is a fast console program, computing all prime numbers between a specified minimum and maximum value of range [0, 2⁶⁴ - 1].

Usage

• Build: gcc main.c -O3 -lm -o qprimes
• Run qprimes MIN MAX to generate prime numbers between [MIN, MAX].
• MIN, MAX can be expressed in decimal form or, if preceded by 0x, in haxadecimal form.
• Run qprimes without arguments for more options.

Quick Example

$ git clone https://github.com/johsteffens/qprimes
$ cd qprimes
$ gcc main.c -O3 -lm -o qprimes
$ ./qprimes 10000000001099 10000000001199
10000000001141
10000000001161
10000000001177
10000000001191

4 primes between 10000000001099 and 10000000001199
Heap size: 197899 Bytes

Method

qprimes uses a mix of sieving and paging.

First, a list of all primes between 2 and MAX^1/2 is generated. That list is used to determine primes in the desired value range.

Speed and Memory

With n := MAX^1/2 and r := MAX - MIN:

• Processing time is about O( n log log n ) for r << n.
• Memory requirement is about O( n ).

The maximum possible heap memory usage is around 270 MBytes.

Timing Example

Command: qprimes 0xFFFFFFFFFFFFFF00 0xFFFFFFFFFFFFFFFF
This test computes the last few primes below 2⁶⁴. It is the worst case for the gven prime window size. Smaller primes will compute faster.

Platform	Time
AMD RyzenTM 9 7950X	9 seconds
IntelR CoreTM i7 6700	22 seconds
Raspberry Pi 3 Model B+	250 seconds
Raspberry Pi 2 Model B	370 seconds

Motivation

Prime numbers are needed in various disciplines of numerical processing. I wrote this generator because arbitrary prime numbers above, say 2⁴⁰, were not so easy to find on public sources.

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_{© Johannes B. Steffens}