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, 8 <= SIZE <= 4096. 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 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>

                                                   02/05/2022                                      PRIMESIEVE(1)