However, some bounds on π(x) are known, for instance Pierre Dusart's
Prime Minister | Prime Minister of the United Kingdom | Prime Minister of Canada | Prime Minister of Australia | prime minister | Prime Minister of India | Prime Minister of Japan | Prime Minister of Israel | Prime Minister of Singapore | Prime Minister of Malaysia | Prime Minister of Pakistan | Prime minister | Deputy Prime Minister | Prime Minister of New Zealand | prime time | Prime Suspect | Prime Minister of Italy | Optimus Prime | Prime Suspect (UK TV series) | Prime Minister of Spain | Prime Minister's Office | Prime Minister of Sweden | Prime Minister of Northern Ireland | Lucky Number Slevin | Reynolds number | Prime Minister of Russia | Prime Minister of Poland | Prime Minister of Norway | Prime Minister of France | Mach number |
20 Charles Pisot, Démonstration élémentaire du théorème des nombres premiers, d'après Selberg et Erdös (prime number theorem)