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.\" Title: primesieve
.\" Author: [see the "AUTHOR" section]
.\" Generator: DocBook XSL Stylesheets vsnapshot
.\" Date: 02/17/2024
.\" Manual: \ \&
.\" Source: \ \&
.\" Language: English
.\"
.TH "PRIMESIEVE" "1" "02/17/2024" "\ \&" "\ \&"
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.SH "NAME"
primesieve \- generate prime numbers
.SH "SYNOPSIS"
.sp
\fBprimesieve\fR [\fISTART\fR] \fISTOP\fR [\fIOPTION\fR]\&...
.SH "DESCRIPTION"
.sp
Generate the prime numbers and/or prime k\-tuplets inside [\fISTART\fR, \fISTOP\fR] (< 2^64) using the segmented sieve of Eratosthenes\&. primesieve includes a number of extensions to the sieve of Eratosthenes which significantly improve performance: multiples of small primes are pre\-sieved, it uses wheel factorization to skip multiples with small prime factors and it uses the bucket sieve algorithm which improves cache efficiency when sieving > 2^32\&. primesieve is also multi\-threaded, it uses all available CPU cores by default for counting primes and for finding the nth prime\&.
.sp
The segmented sieve of Eratosthenes has a runtime complexity of O(n log log n) operations and it uses O(n^(1/2)) bits of memory\&. More specifically primesieve uses 8 bytes per sieving prime, hence its memory usage can be approximated by PrimePi(n^(1/2)) * 8 bytes (per thread)\&.
.SH "OPTIONS"
.PP
\fB\-c\fR[\fINUM+\fR], \fB\-\-count\fR[=\fINUM+\fR]
.RS 4
Count primes and/or prime k\-tuplets, 1 <=
\fINUM\fR
<= 6\&. Count primes:
\fB\-c\fR
or
\fB\-\-count\fR, count twin primes:
\fB\-c2\fR
or
\fB\-\-count=2\fR, count prime triplets:
\fB\-c3\fR
or
\fB\-\-count=3\fR, \&... You can also count primes and prime k\-tuplets at the same time, e\&.g\&.
\fB\-c123\fR
counts primes, twin primes and prime triplets\&.
.RE
.PP
\fB\-\-cpu\-info\fR
.RS 4
Print CPU information: CPU name, frequency, number of cores, cache sizes, \&...
.RE
.PP
\fB\-d, \-\-dist\fR=\fIDIST\fR
.RS 4
Sieve the interval [\fISTART\fR,
\fISTART\fR
+
\fIDIST\fR]\&.
.RE
.PP
\fB\-h, \-\-help\fR
.RS 4
Print this help menu\&.
.RE
.PP
\fB\-n, \-\-nth\-prime\fR
.RS 4
Find the nth prime, e\&.g\&. 100
\fB\-n\fR
finds the 100th prime\&. If 2 numbers
\fIN\fR
\fISTART\fR
are provided finds the nth prime >
\fISTART\fR, e\&.g\&. 2 100
\fB\-n\fR
finds the 2nd prime > 100\&.
.RE
.PP
\fB\-\-no\-status\fR
.RS 4
Turn off the progressing status\&.
.RE
.PP
\fB\-p\fR[\fINUM\fR], \fB\-\-print\fR[=\fINUM\fR]
.RS 4
Print primes or prime k\-tuplets, 1 <=
\fINUM\fR
<= 6\&. Print primes:
\fB\-p\fR, print twin primes:
\fB\-p2\fR, print prime triplets:
\fB\-p3\fR, \&...
.RE
.PP
\fB\-q, \-\-quiet\fR
.RS 4
Quiet mode, prints less output\&.
.RE
.PP
\fB\-R, \-\-RiemannR\fR
.RS 4
Approximate PrimePi(x) using the Riemann R function: R(x)\&.
.RE
.PP
\fB\-\-RiemannR\-inverse\fR
.RS 4
Approximate the nth prime using the inverse Riemann R function: R^\-1(x)\&.
.RE
.PP
\fB\-s, \-\-size\fR=\fISIZE\fR
.RS 4
Set the size of the sieve array in KiB, 16 <=
\fISIZE\fR
<= 8192\&. By default primesieve uses a sieve size that matches your CPU\(cqs L1 cache size (per core) or is slightly smaller than your CPU\(cqs L2 cache size\&. This setting is crucial for performance, on exotic CPUs primesieve sometimes fails to determine the CPU\(cqs cache sizes which usually causes a big slowdown\&. In this case you can get a significant speedup by manually setting the sieve size to your CPU\(cqs L1 or L2 cache size (per core)\&.
.RE
.PP
\fB\-S, \-\-stress\-test\fR[=\fIMODE\fR]
.RS 4
Run a stress test\&. The
\fIMODE\fR
can be either CPU (default) or RAM\&. The CPU
\fIMODE\fR
uses little memory (< 5 MiB per thread) and puts the highest load on the CPU\&. The RAM
\fIMODE\fR
on the other hand uses much more memory than the CPU
\fIMODE\fR
(each thread uses about 1\&.16 GiB), but the CPU usually won\(cqt get as hot as in the CPU
\fIMODE\fR\&. Stress testing keeps on running until either a miscalculation occurs (due to a hardware issue) or the timeout expires\&. The default timeout is 24 hours, the timeout can be changed using the
\fB\-\-timeout=SECS\fR
option\&. By default the stress test uses a number of threads that matches the number of CPU cores, the number of threads can be changed using the
\fB\-\-threads=NUM\fR
option\&.
.RE
.PP
\fB\-\-test\fR
.RS 4
Run various correctness tests (< 1 minute)\&.
.RE
.PP
\fB\-t, \-\-threads\fR=\fINUM\fR
.RS 4
Set the number of threads, 1 <=
\fINUM\fR
<= CPU cores\&. By default primesieve uses all available CPU cores for counting primes and for finding the nth prime\&.
.RE
.PP
\fB\-\-time\fR
.RS 4
Print the time elapsed in seconds\&.
.RE
.PP
\fB\-\-timeout\fR=\fISECS\fR
.RS 4
Set the stress test timeout in seconds\&. Units of time for seconds, minutes, hours, days and years are also supported with the suffix s, m, h, d or y\&. E\&.g\&.
\fB\-\-timeout 10m\fR
sets a timeout of 10 minutes\&. The default stress test timeout is 24 hours\&.
.RE
.PP
\fB\-v, \-\-version\fR
.RS 4
Print version and license information\&.
.RE
.SH "EXAMPLES"
.PP
\fBprimesieve 1000\fR
.RS 4
Count the primes <= 1000\&.
.RE
.PP
\fBprimesieve 1e6 \-\-print\fR
.RS 4
Print the primes <= 10^6\&.
.RE
.PP
\fBprimesieve 1e6 \-\-print > primes\&.txt\fR
.RS 4
Store the primes <= 10^6 in a text file\&.
.RE
.PP
\fBprimesieve 2^32 \-\-print=2\fR
.RS 4
Print the twin primes <= 2^32\&.
.RE
.PP
\fBprimesieve 1e16 \-\-dist=1e10 \-\-threads=1\fR
.RS 4
Count the primes inside [10^16, 10^16 + 10^10] using a single thread\&.
.RE
.SH "HOMEPAGE"
.sp
https://github\&.com/kimwalisch/primesieve
.SH "AUTHOR"
.sp
Kim Walisch