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### Sum of inverse primes

The sum of the reciprocals of all **prime numbers** is a divergent series.

##### Explanation

Leonhardt Euler has calculated the series of reciprocals of primes as

This means that there are infinitely many primes. This proof was given by Euclid on another way before. The geometric series

is convergent. Primes occur therefore relatively frequent under the natural numbers.

## HistoryThe Swiss mathematician Leonhardt Euler (1707 - 1783) used this to support the proof of the Greek mathematician Euclid (around 300 BC). |