1PRIMESIEVE(1)                                                    PRIMESIEVE(1)
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NAME

6       primesieve - generate prime numbers
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SYNOPSIS

9       primesieve [START] STOP [OPTION]...
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DESCRIPTION

12       Generate the prime numbers and/or prime k-tuplets inside [START, STOP]
13       (< 2^64) using the segmented sieve of Eratosthenes. primesieve includes
14       a number of extensions to the sieve of Eratosthenes which significantly
15       improve performance: multiples of small primes are pre-sieved, it uses
16       wheel factorization to skip multiples with small prime factors and it
17       uses the bucket sieve algorithm which improves cache efficiency when
18       sieving > 2^32. primesieve is also multi-threaded, it uses all
19       available CPU cores by default for counting primes and for finding the
20       nth prime.
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22       The segmented sieve of Eratosthenes has a runtime complexity of O(n log
23       log n) operations and it uses O(n^(1/2)) bits of memory. More
24       specifically primesieve uses 8 bytes per sieving prime, hence its
25       memory usage can be approximated by PrimePi(n^(1/2)) * 8 bytes (per
26       thread).
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OPTIONS

29       -c[NUM+], --count[=NUM+]
30           Count primes and/or prime k-tuplets, 1 <= NUM <= 6. Count primes:
31           -c or --count, count twin primes: -c2 or --count=2, count prime
32           triplets: -c3 or --count=3, ... You can also count primes and prime
33           k-tuplets at the same time, e.g.  -c123 counts primes, twin primes
34           and prime triplets.
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36       --cpu-info
37           Print CPU information: CPU name, frequency, number of cores, cache
38           sizes, ...
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40       -d, --dist=DIST
41           Sieve the interval [START, START + DIST].
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43       -h, --help
44           Print this help menu.
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46       -n, --nth-prime
47           Find the nth prime, e.g. 100 -n finds the 100th prime. If 2 numbers
48           N START are provided finds the nth prime > START, e.g. 2 100 -n
49           finds the 2nd prime > 100.
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51       --no-status
52           Turn off the progressing status.
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54       -p[NUM], --print[=NUM]
55           Print primes or prime k-tuplets, 1 <= NUM <= 6. Print primes: -p,
56           print twin primes: -p2, print prime triplets: -p3, ...
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58       -q, --quiet
59           Quiet mode, prints less output.
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61       -s, --size=SIZE
62           Set the size of the sieve array in KiB, 8 <= SIZE <= 4096. By
63           default primesieve uses a sieve size that matches your CPU’s L1
64           cache size (per core) or is slightly smaller than your CPU’s L2
65           cache size. This setting is crucial for performance, on exotic CPUs
66           primesieve sometimes fails to determine the CPU’s cache sizes which
67           usually causes a big slowdown. In this case you can get a
68           significant speedup by manually setting the sieve size to your
69           CPU’s L1 or L2 cache size (per core).
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71       --test
72           Run various sieving tests.
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74       -t, --threads=NUM
75           Set the number of threads, 1 <= NUM <= CPU cores. By default
76           primesieve uses all available CPU cores for counting primes and for
77           finding the nth prime.
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79       --time
80           Print the time elapsed in seconds.
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82       -v, --version
83           Print version and license information.
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EXAMPLES

86       primesieve 1000
87           Count the primes <= 1000.
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89       primesieve 1e6 --print
90           Print the primes <= 10^6.
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92       primesieve 2^32 --print=2
93           Print the twin primes <= 2^32.
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95       primesieve 1e16 --dist=1e10 --threads=1
96           Count the primes inside [10^16, 10^16 + 10^10] using a single
97           thread.
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HOMEPAGE

100       https://github.com/kimwalisch/primesieve
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AUTHOR

103       Kim Walisch <kim.walisch@gmail.com>
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107                                  01/30/2022                     PRIMESIEVE(1)