http://qs321.pair.com?node_id=1214638

in reply to Sieve of Eratosthenes with closures

This is a great idea. I always wanted to implement a sieve that can just go on finding new primes, i.e. without specifying a maximum up to which the sieving will be conducted. This would require not only to store the primes up to a point but also kind of the largest multiple of each prime up to that point. Also, I think using the modulus operator % violates the sieving philosophy. I never was able to make it work as I got confused keeping the primes and the multiples.

Using closures is ideal for that. Every time one finds a new prime, one generates a new sifter that is responsible for that prime and to store the progress to date. Here is my formulation:

```use strict;
use warnings;

sub sifter {
my \$p = shift;
my \$c = \$p;
return sub { \$c += \$p while \$c < \$_[0]; return \$c-\$_[0]; }
}

my @sieves;
my \$n = 1;

loop: while( \$n++ ){
\$_->( \$n ) or next loop for @sieves;
push @sieves, sifter( \$n );
print "\$n\n";
}