Let’s define the quantity , and assume Cramer’s conjecture. Then . Let’s denote by the event is -central, and by the event is a couple of twin primes. Then from de Bayes’ theorem, one gets , since if is the half sum of a couple of twin primes, then necessarily is -central. But is equal to the ratio of the number of quantities such that is the half sum of twin primes to the number as defined above, hence . As , one finally gets . Hence the assumption of Cramer’s conjecture implies that there are infinitely many twin primes.