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Mersenne Primes (Part 2)

In this video we give a proof of the Euclid-Euler Theorem. It follows from this theorem that there are infinitely many Mersenne Primes if and only if there are infinitely many even perfect numbers. Timestamps 00:00 Recap 01:40 Euclid-Euler theorem 02:30 Sufficiency 05:26 Necessity The sufficiency part is briefly mentioned in Euler's first paper in number theory 'Observationes de theoremate quodam Fermatiano aliisque ad numeros primos spectantibus' (E026 in Eneström index.) The necessity part is proved in Section 8 of Euler's paper 'De numeris amicabilibus' (E798).