Olivier Ramaré

Olivier Ramaré

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Olivier Ramaré is a French
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

 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....

 who teaches at the Université des Sciences et Technologies de Lille
Université des Sciences et Technologies de Lille
The Université Lille 1 is a French university located on a dedicated main campus in Villeneuve d'Ascq with 20,000 full-time students plus 14,500 students in continuing education...

.

In 1995, he sharpened earlier work on Schnirelmann's theorem by proving
Mathematical proof
In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single...

 that every even number is a sum of at most six prime
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...

s. This result may be compared with Goldbach's conjecture
Goldbach's conjecture
Goldbach's conjecture is one of the oldest unsolved problems in number theory and in all of mathematics. It states:A Goldbach number is a number that can be expressed as the sum of two odd primes...

, which states that every even number except 2 is the sum of two primes. The truth of Ramaré's result for all sufficiently large even numbers is a consequence of Vinogradov's theorem
Vinogradov's theorem
In number theory, Vinogradov's theorem implies that any sufficiently large odd integer can be written as a sum of three prime numbers. It is a weaker form of Goldbach's conjecture, which would imply the existence of such a representation for all odd integers greater than five. It is named after...

, whereas the full result follows from Goldbach's weak conjecture
Goldbach's weak conjecture
In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that:...

.