77 lines
2.7 KiB
Factor
77 lines
2.7 KiB
Factor
USING: help.markup help.syntax kernel math sequences ;
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IN: math.primes
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{ next-prime prime? } related-words
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HELP: next-prime
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{ $values { "n" integer } { "p" "a prime number" } }
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{ $description "Return the next prime number greater than " { $snippet "n" } "." } ;
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HELP: prime?
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{ $values { "n" integer } { "?" boolean } }
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{ $description "Test if an integer is a prime number." } ;
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{ nprimes primes-upto primes-between } related-words
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HELP: nprimes
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{ $values { "n" "a non-negative integer" } { "seq" sequence } }
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{ $description "Return a sequence containing the " { $snippet "n" } " first primes numbers." } ;
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HELP: primes-upto
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{ $values { "n" integer } { "seq" sequence } }
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{ $description "Return a sequence containing all the prime numbers smaller or equal to " { $snippet "n" } "." } ;
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HELP: primes-between
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{ $values { "low" integer } { "high" integer } { "seq" sequence } }
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{ $description "Return a sequence containing all the prime numbers between " { $snippet "low" } " and " { $snippet "high" } "." } ;
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HELP: find-relative-prime
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{ $values
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{ "n" integer }
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{ "p" integer }
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}
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{ $description "Returns a number that is relatively prime to " { $snippet "n" } "." } ;
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HELP: find-relative-prime*
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{ $values
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{ "n" integer } { "guess" integer }
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{ "p" integer }
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}
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{ $description "Returns a number that is relatively prime to " { $snippet "n" } ", starting by trying " { $snippet "guess" } "." } ;
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HELP: random-prime
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{ $values
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{ "numbits" integer }
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{ "p" integer }
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}
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{ $description "Returns a prime number exactly " { $snippet "numbits" } " bits in length, with the topmost bit set to one." } ;
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HELP: unique-primes
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{ $values
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{ "n" integer }
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{ "numbits" integer }
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{ "seq" sequence }
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}
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{ $description "Generates a sequence of " { $snippet "n" } " unique prime numbers with exactly " { $snippet "numbits" } " bits." } ;
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ARTICLE: "math.primes" "Prime numbers"
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"The " { $vocab-link "math.primes" } " vocabulary implements words related to prime numbers. Several useful vocabularies exist for testing primality. The Sieve of Eratosthenes in " { $vocab-link "math.primes.erato" } " is useful for testing primality below five million. For larger integers, " { $vocab-link "math.primes.miller-rabin" } " is a fast probabilistic primality test. The " { $vocab-link "math.primes.lucas-lehmer" } " vocabulary implements an algorithm for finding huge Mersenne prime numbers." $nl
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"Testing if a number is prime:"
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{ $subsections prime? }
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"Generating prime numbers:"
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{ $subsections
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next-prime
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primes-upto
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primes-between
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random-prime
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}
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"Generating relative prime numbers:"
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{ $subsections
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find-relative-prime
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find-relative-prime*
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}
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"Make a sequence of random prime numbers:"
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{ $subsections unique-primes } ;
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ABOUT: "math.primes"
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