Divergence of the sum of the reciprocals of the primes
Serie de los inversos de los números primos
- Date
- c. 1737 · confidence low
- Place
- Saint Petersburg, Russia
- Credited to
- Leonhard Euler
- Field
- Knowledge & symbols
What was discovered
Proof that the sum of the reciprocals of all prime numbers diverges, due to Leonhard Euler, revealing that the primes are in some sense "more numerous" than, say, the perfect squares.
What it led to
- A new, analytic-methods proof of the infinitude of primes
- Starting point of analytic number theory
- Forerunner of the later prime number theorem