A fast algorithm to count the number of primes up to N. Implemented in JavaScript.
The C++ Primesieve implementation claims that "It counts the primes below 10^10 in just 0.4 seconds on an Intel Core i7-6700 CPU (4 x 3.4 GHz)." In comparison, our single-threaded, unoptimized JavaScript implementation counts the primes below 10^10 in 0.5 seconds on an Intel Core i7 (4 x 2.9 GHz).
A C / C++ / Rust / implementation with fast integer division probably beats the "Priemsieve" implementation. Additionally, our algorithm is highly parallelizable. Probably, even simple multi-threading leads to further significant performance improvements.
You can run the benchmarks on your machine. Open the console. For example, the commands
benchmark(8, 5761455)
benchmark(9, 50847534)
benchmark(10, 455052511)
count the primes up to 10^8, 10^9, 10^10 and assert correctness.