He was born in Schroda in the Grand Duchy of Posen, Kingdom of Prussia (now Środa Wielkopolska, Poland) and died in Vienna, Austria.

The Mertens conjecture concerning its growth, conjecturing it bounded by x1/2, which would have implied the Riemann hypothesis, is now known to be false (Odlyzko and te Riele, 1985).

Mertens's theorems are three 1874 results related to the density of prime numbers.

Erwin Schrödinger was taught calculus and algebra by Mertens.

[1] His memory is honoured by the Franciszek Mertens Scholarship granted (from 2017) to those outstanding pupils of foreign secondary schools who wish to study at the Faculty of Mathematics and Computer Science of the Jagiellonian University in Kraków and were finalists of the national-level mathematics, or computer science olympiads, or they have participated in one of the following international olympiads: in mathematics (IMO), computer science (IOI), artificial intelligence (IOAI), astronomy (IAO), astronomy and astrophysics (IOAA), physics (IPhO), linguistics (IOL), European Girls' Mathematical Olympiad (EGMO), European Girls’ Olympiad in Informatics (EGOI), Romanian Masters of Mathematics (RMM), Romanian Masters of Informatics (RMI) or International Zhautykov Olympiad (IZhO).