--- /dev/null
+Samuel Tardieu
--- /dev/null
+USING: help.markup help.syntax ;
+IN: math.primes
+
+{ next-prime prime? } related-words
+
+HELP: next-prime
+{ $values { "n" "a positive integer" } { "p" "a prime number" } }
+{ $description "Return the next prime number greater than " { $snippet "n" } "." } ;
+
+HELP: prime?
+{ $values { "n" "an integer" } { "?" "a boolean" } }
+{ $description "Test if an integer is a prime number." } ;
+
+{ lprimes lprimes-from primes-upto primes-between } related-words
+
+HELP: lprimes
+{ $values { "list" "a lazy list" } }
+{ $description "Return a sorted list containing all the prime numbers." } ;
+
+HELP: lprimes-from
+{ $values { "n" "an integer" } { "list" "a lazy list" } }
+{ $description "Return a sorted list containing all the prime numbers greater or equal to " { $snippet "n" } "." } ;
+
+HELP: primes-upto
+{ $values { "n" "an integer" } { "seq" "a sequence" } }
+{ $description "Return a sequence containing all the prime numbers smaller or equal to " { $snippet "n" } "." } ;
+
+HELP: primes-between
+{ $values { "low" "an integer" } { "high" "an integer" } { "seq" "a sequence" } }
+{ $description "Return a sequence containing all the prime numbers between " { $snippet "low" } " and " { $snippet "high" } "." } ;
--- /dev/null
+USING: arrays math.primes tools.test lazy-lists ;
+
+{ 1237 } [ 1234 next-prime ] unit-test
+{ f t } [ 1234 prime? 1237 prime? ] unit-test
+{ { 2 3 5 7 11 13 17 19 23 29 } } [ 10 lprimes ltake list>array ] unit-test
+{ { 101 103 107 109 113 } } [ 5 100 lprimes-from ltake list>array ] unit-test
+{ { 1000117 1000121 } } [ 2 1000100 lprimes-from ltake list>array ] unit-test
+{ { 999983 1000003 } } [ 2 999982 lprimes-from ltake list>array ] unit-test
+{ { 2 3 5 7 } } [ 10 primes-upto >array ] unit-test
+{ { 999983 1000003 } } [ 999982 1000010 primes-between >array ] unit-test
--- /dev/null
+! Copyright (C) 2007 Samuel Tardieu.
+! See http://factorcode.org/license.txt for BSD license.
+USING: combinators kernel lazy-lists math math.functions math.miller-rabin
+ math.primes.list math.ranges sequences sorting ;
+IN: math.primes
+
+<PRIVATE
+
+: find-prime-miller-rabin ( n -- p )
+ dup miller-rabin [ 2 + find-prime-miller-rabin ] unless ; foldable
+
+PRIVATE>
+
+: next-prime ( n -- p )
+ dup 999983 < [
+ primes-under-million [ [ <=> ] binsearch 1+ ] keep nth
+ ] [
+ next-odd find-prime-miller-rabin
+ ] if ; foldable
+
+: prime? ( n -- ? )
+ dup 1000000 < [
+ dup primes-under-million [ <=> ] binsearch* =
+ ] [
+ miller-rabin
+ ] if ; foldable
+
+: lprimes ( -- list )
+ 0 primes-under-million seq>list
+ 1000003 [ 2 + find-prime-miller-rabin ] lfrom-by
+ lappend ;
+
+: lprimes-from ( n -- list )
+ dup 3 < [ drop lprimes ] [ 1- next-prime [ next-prime ] lfrom-by ] if ;
+
+: primes-upto ( n -- seq )
+ {
+ { [ dup 2 < ] [ drop { } ] }
+ { [ dup 1000003 < ]
+ [ primes-under-million [ [ <=> ] binsearch 1+ 0 swap ] keep <slice> ] }
+ { [ t ]
+ [ primes-under-million 1000003 lprimes-from
+ rot [ <= ] curry lwhile list>array append ] }
+ } cond ; foldable
+
+: primes-between ( low high -- seq )
+ primes-upto
+ >r 1- next-prime r>
+ [ [ <=> ] binsearch ] keep [ length ] keep <slice> ; foldable
--- /dev/null
+Prime numbers test and generation
+