Applications
- Brun's theorem: the sum of the reciprocals of the twin primes converges;
- Schnirelmann's theorem: every even number is a sum of at most C primes (where C can be taken to be 6);
- There are infinitely many pairs of integers differing by 2, where each of the member of the pair is the product of at most 9 primes;
- Every even number is the sum of two numbers each of which is the product of at most 9 primes.
The last two results were superseded by Chen's theorem.
Read more about this topic: Brun Sieve