# There are Infinitely Many Primes - II

In Part–I of this article we dwelt on various proofs that show the infinitude of the primes. These were mostly based on Euclid’s proof — the one for which G H Hardy had such high praise. All of these start by assuming that there exists a ‘last prime’. Then in a clever way they construct a number whose prime factors exceed this last prime. The one proof discussed which does not belong to this category is Pólya’s; he makes use of the Fermat numbers. The first proof of a completely different nature is Euler’s; he shows that the sum of the reciprocals of the primes is infinite, and hence there must exist infinitely many primes. In Part–II we dwell on this proof...