Primery

Primery is used to generate prime numbers in a specified range [x, y]. It also measures the time each algorithm needs to generate the prime numbers. It`s planned to expand the usage for checking primes as well and perfoming other operations.

Supported algorithms

Algorithm	Complexity
Trial Division	O(n*sqrt(n))
Sieve of Eratosthenes	O(n*log(log(n)))
Sieve of Sundaram	O(n*log(n))
Sieve of Atkin	O(n))

Time comparisons

Hardware:

CPU: 11th Gen Intel© Core™ i7-11800H @ 2.30GHz × 8
GPU: Intel Corporation TigerLake-H GT1 [UHD Graphics]

Single threaded:

n	Sieve of Eratosthenes	Sieve of Sundaram	Sieve of Atkin
10⁵	0.718 ms	0.602 ms	0.936 ms
10⁶	7.544 ms	6.956 ms	8.386 ms
10⁷	66.149 ms	65.015 ms	62.988 ms
10⁸	0.947 s	1.007 s	0.837 s
10⁹	10.956 s	16.559 s	8.839 s

Mulit threaded:

n	Sieve of Eratosthenes	Sieve of Sundaram	Sieve of Atkin
10⁵	3.197 ms	27.105 ms	10.941 ms
10⁶	11.735 ms	140.159 ms	40.063 ms
10⁷	62.772 ms	1.195 s	122.007 ms
10⁸	0.49 s	11.984 s	0.511 s
10⁹	7.284 s	-	3.903 s

Conclusion:

Based on the data in the tables, it appears that the Sieve of Atkin is the fastest algorithm for generating prime numbers in both single-threaded and multi-threaded environments. In single-threaded mode, it is faster than the other two algorithms for all values of n tested. In multi-threaded mode, it is still the fastest algorithm for n up to 10⁸, and is competitive with the Sieve of Eratosthenes for n = 10⁹. The Sieve of Sundaram is slower than the other two algorithms in both single-threaded and multi-threaded mode. For large inputs, multithreading gives a great perfomance boost for generating prime numbers.

Makefile

#### primery v1.3 ####

Available targets:

build                          Build software
clean                          Remove program and output files
help                           Get help for Makefile
install                        Install software globally
uninstall                      Uninstall software

Usage

USAGE: primery [Options] {algorithm}

EXAMPLE: primery -i [234,100000] -t ms -m p sieveOfEratosthenes

SUPPORTED ALGORITHMS:
    { td  | trialDivision }
    { soe | sieveOfEratosthenes }
    { sos | sieveOfSundaram }
    { soa | sieveOfAtkin }

OPTIONS:
    -h, --help: Get help for the program
    -o, --output: Specify an output file for the generated prime numbers (default is primes.txt)
    -m, --mode: Specify a mode for generating prime numbers [s | single, p | parallel] (default is single)
    -t, --time: Specify time format [ns | nanoseconds, ms | milliseconds, s | seconds] (default is milliseconds)
    -i, --interval: Specify interval to generate prime numbers in format [start,end] (default is [2,1000])

Docker

To build the docker image, run the following command:

docker build -t primery .

To run the docker image, run the following command:

docker run --rm -v $(pwd)/.:/primery primery -i [234,100000] -t ms -m p sieveOfEratosthenes