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.
-R, --RiemannR
Approximate PrimePi(x) using the Riemann R function:
R(x).
--RiemannR-inverse
Approximate the nth prime using the inverse Riemann R
function: R^-1(x).
-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).
-S, --stress-test[=MODE]
Run a stress test. The MODE can be either CPU
(default) or RAM. The CPU MODE uses little memory (< 5 MiB per
thread) and puts the highest load on the CPU. The RAM MODE on the other
hand uses much more memory than the CPU MODE (each thread uses about
1.16 GiB), but the CPU usually won’t get as hot as in the CPU
MODE. 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 --timeout=SECS
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
--threads=NUM option.
--test
Run various correctness tests (< 1 minute).
-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.
--timeout=SECS
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. --timeout 10m sets a timeout of 10 minutes. The
default stress test timeout is 24 hours.
-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.
AUTHOR¶
Kim Walisch <kim.walisch@gmail.com>
