PRIMESIEVE(1) PRIMESIEVE(1)
NAME
primesieve - generate prime numbers
SYNOPSIS
primesieve [START] STOP [OPTION]...
DESCRIPTION
Generate the prime numbers and/or prime k-tuplets inside [START, STOP]
(< 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.
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).
OPTIONS
-c[NUM+], --count[=NUM+]
Count primes and/or prime k-tuplets, 1 <= NUM <= 6. Count primes:
-c or --count, count twin primes: -c2 or --count=2, count prime
triplets: -c3 or --count=3, ... You can also count primes and prime
k-tuplets at the same time, e.g. -c123 counts primes, twin primes
and prime triplets.
--cpu-info
Print CPU information: CPU name, frequency, number of cores, cache
sizes, ...
-d, --dist=DIST
Sieve the interval [START, START + DIST].
-h, --help
Print this help menu.
-n, --nth-prime
Find the nth prime, e.g. 100 -n finds the 100th prime. If 2 numbers
N START are provided finds the nth prime > START, e.g. 2 100 -n
finds the 2nd prime > 100.
--no-status
Turn off the progressing status.
-p[NUM], --print[=NUM]
Print primes or prime k-tuplets, 1 <= NUM <= 6. Print primes: -p,
print twin primes: -p2, print prime triplets: -p3, ...
-q, --quiet
Quiet mode, prints less output.
-s, --size=SIZE
Set the size of the sieve array in KiB, 16 <= SIZE <= 8192. By
default primesieve uses a sieve size that matches your CPU’s L1
cache size (per core) or is slightly smaller than your CPU’s L2
cache size. This setting is crucial for performance, on exotic CPUs
primesieve sometimes fails to determine the CPU’s 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’s L1 or L2 cache size (per core).
--test
Run various sieving tests.
-t, --threads=NUM
Set the number of threads, 1 <= NUM <= CPU cores. By default
primesieve uses all available CPU cores for counting primes and for
finding the nth prime.
--time
Print the time elapsed in seconds.
-v, --version
Print version and license information.
EXAMPLES
primesieve 1000
Count the primes <= 1000.
primesieve 1e6 --print
Print the primes <= 10^6.
primesieve 1e6 --print > primes.txt
Store the primes <= 10^6 in a text file.
primesieve 2^32 --print=2
Print the twin primes <= 2^32.
primesieve 1e16 --dist=1e10 --threads=1
Count the primes inside [10^16, 10^16 + 10^10] using a single
thread.
HOMEPAGE
https://github.com/kimwalisch/primesieve
AUTHOR
Kim Walisch <kim.walisch@gmail.com>
12/21/2022 PRIMESIEVE(1)
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