Number of primes less than or equal to n


          n   

 



This Javascript calculates the number of prime numbers less than or equal to n using the Sieve of Eratosthenes algorithm.

An estimated number is given by n/(log n - 1), which is related to the prime number theorem.

The script also gives an example of Goldbach's conjectures. Goldbach's strong conjecture states that any even number can be expressed as the sum of two prime numbers, and Goldbach's weak conjecture states that any odd number can be expressed as the sum of three prime numbers. I have a rather elegant proof of these conjectures, but don't have enough room to write it down here.



Home page Email December 28, 2012