Andy Loo is a Hong Kong

Hong Kong

Hong Kong is one of two Special Administrative Regions of the People's Republic of China , the other being Macau. A city-state situated on China's south coast and enclosed by the Pearl River Delta and South China Sea, it is renowned for its expansive skyline and deep natural harbour...

 mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 working primarily in number theory

Number theory

Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...

. He is also a successful participant of the International Physics Olympiad

International Physics Olympiad

The International Physics Olympiad is an annual physics competition for high school students. It is one of the International Science Olympiads. The first IPhO was held in Warsaw, Poland in 1967....

.

Research

In 2011, as a high school student at St. Paul's Co-educational College, Hong Kong

St. Paul's Co-educational College

St. Paul's Co-educational College , is located at 33 MacDonnell Road, Mid-levels, Hong Kong....

, Loo used elementary techniques

Elementary proof

In mathematics, an elementary proof is a mathematical proof that only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. For some time it was thought that certain theorems, like the prime number theorem, could only be...

 to prove that there exists a prime number

Prime number

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...

 between 3n and 4n for all positive integers n, and that, furthermore, the number of primes between 3n and 4n goes to infinity

Infinity

Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...

 as n tends to infinity, thereby generalizing previous results of Erdős

Paul Erdos

Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...

 and Ramanujan

Srinivasa Ramanujan

Srīnivāsa Aiyangār Rāmānujan FRS, better known as Srinivasa Iyengar Ramanujan was a Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions...

. See Bertrand's Postulate for details.

Physics Olympiad

Loo participated in the International Physics Olympiad

International Physics Olympiad

The International Physics Olympiad is an annual physics competition for high school students. It is one of the International Science Olympiads. The first IPhO was held in Warsaw, Poland in 1967....

 twice, winning a silver medal and a gold medal in 2010 and 2011 respectively.

See also

• St. Paul's Co-educational College
  St. Paul's Co-educational College
  St. Paul's Co-educational College , is located at 33 MacDonnell Road, Mid-levels, Hong Kong....
  
  
• Bertrand's Postulate
• International Physics Olympiad
  International Physics Olympiad
  The International Physics Olympiad is an annual physics competition for high school students. It is one of the International Science Olympiads. The first IPhO was held in Warsaw, Poland in 1967....