00:01
The statement which is given to us in the question is known as the divergence of the sum of the reciprocals.
00:19
Reciprocals, i'll just write it.
00:24
Okay, this is r over here in the first place of the primes.
00:32
Okay, and this is also one of the most fascinating resulting number theory.
00:37
Theory.
00:37
It states that the sum of the reciprocals of all the prime numbers, that is like 1 by 2, 1 by 3, plus 1 by 5, up to so on, they diverges meaning it grows without bound and does not approach a finite limit.
00:54
So this result is actually closely related to prove that there are infinitely many primes.
01:00
The divergence of the series, the the divergence of this series provides a stronger result.
01:15
Not only there are infinitely many primes, but they are dense enough that the sum diverges...