## Riemann's: "On the Number of Prime Numbers less than a Given Quantity"

This is the first page of Bernhard Riemann's autograph of his article "On the Number of Prime Numbers less than a Given Quantity" ("Über die Anzahl der Primzahlen unter einer gegebenen Grösse."), which appeared in the *Monatsberichte der Berliner Akademie*, in November 1859. In that article Riemann proves that the zeta function, which became known as the "Riemann zeta function", has a meromorphic continuation to the whole complex plane, has a simple pole at s=1 and no other poles. Furthermore, Riemann relates the zeros of the zeta function to the number of primes that are less or equal to a given quantity, and states his famous conjecture: that all (non-trivial) zeros have real part 1/2. Riemann continues: "Certainly one would wish for a strict proof here; I have meanwhile temporarily put aside the search for this after some fleeting futile attempts ..."

**Credits:** The manuscript of Riemann's 1859 paper resides in the Manuscript Department of the Niederschsische Staats- und Universitetsbibliothek Gottingen (shelfmark: Cod. Ms. B. Riemann 3). The photos of Riemann's manuscript on this site are courtesy of the Gottingen Library.