    Sentence 1: What property of the harmonic  series 1+ 1/2 + 1/3 + 1/4 + ... shows thot  there is an infinite number of primes?    Sentence 2: However, the harmonic series  1+ 1/2 + 13+ 14 +... diverges (ie.  exceeds any given number), so there must  be infinitely many primes.    2