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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). |