Goldbach’s Conjecture and Primes Between n and 2n

According to Bertrand-Chebyshev’s theorem there is at least one prime between n and 2n for n > 1. This theorem can be easily proved if one assumes Goldbach’s conjecture.

According to Goldbach’s conjecture every even number is a sum of two primes. This means that we can write

Then either or is . This proves Bertrand-Chebyshev’s theorem.