# Sieve of Eratosthenes (Forth)

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The Sieve of Eratosthenes is an algorithm for rapidly locating all the prime numbers in a certain range of integers. It operates by marking as composite all nontrivial multiples of each prime in sequence until only primes remain unmarked. It is most well-suited to implementation using arrays, which are compact and feature random access.

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This program counts the number of primes up to 7919 (the 1000th prime) using the Sieve of Eratosthenes. The algorithm is optimized by assuming 2 is prime, and thus only examining odd numbers.

**( dup .)** can be uncommented to list the primes found.

<<sieve.fs>>=7919 2/ CONSTANT maxp \ 2/ because we only count odd primes : PRIMES ( -- n ) HERE maxp 1 FILL 1 ( count, including 2 ) maxp 0 DO I HERE + C@ IF I 2* 3 + ( dup .) DUP I + ( prime current ) BEGIN DUP maxp U< WHILE 0 OVER HERE + C! OVER + REPEAT 2DROP 1+ THEN LOOP ; PRIMES . \ 1000

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