#!/bin/bash
# primes.sh: Generate prime numbers, without using arrays.
# Script contributed by Stephane Chazelas.
# This does *not* use the classic "Sieve of Eratosthenes" algorithm,
#+ but instead uses the more intuitive method of testing each candidate number
#+ for factors (divisors), using the "%" modulo operator.
LIMIT=1000 # Primes 2 - 1000
Primes()
{
(( n = $1 + 1 )) # Bump to next integer.
shift # Next parameter in list.
# echo "_n=$n i=$i_"
if (( n == LIMIT ))
then echo $*
return
fi
for i; do # "i" gets set to "@", previous values of $n.
# echo "-n=$n i=$i-"
(( i * i > n )) && break # Optimization.
(( n % i )) && continue # Sift out non-primes using modulo operator.
Primes $n $@ # Recursion inside loop.
return
done
Primes $n $@ $n # Recursion outside loop.
# Successively accumulate positional parameters.
# "$@" is the accumulating list of primes.
}
Primes 1
exit 0
# Uncomment lines 16 and 24 to help figure out what is going on.
# Compare the speed of this algorithm for generating primes
#+ with the Sieve of Eratosthenes (ex68.sh).
# Exercise: Rewrite this script without recursion, for faster execution.