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.

HOMEPAGE

       https://github.com/kimwalisch/primesieve

AUTHOR

       Kim Walisch <kim.walisch@gmail.com>

                                                   03/31/2024                                      PRIMESIEVE(1)