tilly's is a very nice closure implementation. It isn't the fastest pure Perl SoE though. For example, for the first 5761455 primes (primes up to 10^8) tilly's code takes 35.7s on my Macbook. The vector sieve on RosettaCode here takes 37.9s, and the string sieve here takes only 10.2 seconds, albeit with more memory and not an iterator. Using the pure-Perl segmented sieve in Math::Prime::Util::PP takes 7.1 seconds. All of these are terrifically slow compared to C.

If you're looking for even faster SoEs, I recommend Prime Sieve Benchmarks for a list of benchmarks. The C code from AnonymousMonk back in 2003 works fine, but is about 2x slower than the "Trivial 4-line SoE" shown on that page, because it doesn't get the inner loop start correct. Of course they're all in C, though one is built into a Perl module. In general primesieve is the fastest and easiest solution for most projects.

To compare using XS modules, printing primes to 10^8. At this point a majority of our time is actually spent printing, which is why the specialized "print_primes()" routine stomps on everything else, since it has optimized C code (even C's printf is a major bottleneck once the sieving is fast enough).

• 3.4s Math::Prime::XS
• 2.8s Math::Prime::FastSieve
• 2.0s Math::Prime::Util "say for @{primes(1e8)}"
• 1.9s Math::Prime::Util "forprimes { say } 1e8"
• 0.15s Math::Prime::Util "print_primes(1e8);"

Slightly better, here we're naively counting, except for the last one which uses a fast exact prime count method.

• 1.7s Math::Prime::XS
• 0.89s Math::Prime::FastSieve
• 0.39s Math::Prime::Util "$n++ for @{primes(1e8)}"
• 0.18s Math::Prime::Util "forprimes { $n++ } 1e8;"
• 0.00026s Math::Prime::Util "say prime_count(1e8)"