Is there a prize for proving the Goldbach conjecture?

The famous publishing house Faber and Faber are offering a prize of one million dollars to anyone who can prove Goldbach’s Conjecture in the next two years, as long as the proof is published by a respectable mathematical journal within another two years and is approved correct by Faber’s panel of experts.

Why can’t we prove or disprove Goldbach’s Conjecture?

In 1742, Christian Goldbach wrote a letter to his friend, the incomparable Leonhard Euler, proposing that every integer greater than two is the sum of three prime numbers. But there is an infinite number of possibilities, so this approach can never prove the conjecture.

Is there a prize for the Collatz conjecture?

The Collatz conjecture is an unsolved problem in mathematics which introduced by Lothar Collatz in 1937. Although the prize for the proof of this problem is 1 million dollar, nobody has succeeded in proving this conjecture.

Is Hodge conjecture solved?

Some Progress. It turns out that the Hodge Conjecture is true in low dimensions due to a result of Lefschetz in 1924 from before Hodge even made the conjecture in 1950. Lefschetz proved it for codimension 1. In other words, every Hodge class in H²(X, ℚ) is algebraic.

Has Collatz conjecture been proven?

The Collatz conjecture states that the orbit of every number under f eventually reaches 1. And while no one has proved the conjecture, it has been verified for every number less than 268. So if you’re looking for a counterexample, you can start around 300 quintillion. (You were warned!)

Is there any proof of Collatz conjecture?

No, the Collatz conjecture has not been proven, hence the term “conjecture.” In fact, Collatz is nowhere near proved. It is among the least tractable problems in all of mathematics. This combined with the problem’s simple statement makes it quite peculiar.

How do you prove the Hodge conjecture?

The strongest evidence in favor of the Hodge conjecture is the algebraicity result of Cattani, Deligne & Kaplan (1995). Suppose that we vary the complex structure of X over a simply connected base. Then the topological cohomology of X does not change, but the Hodge decomposition does change.

What is Goldbach’s conjecture and why is it important?

Goldbach’s conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that every even whole number greater than 2 is the sum of two prime numbers. The conjecture has been shown to hold for all integers less than 4 × 10 18, but remains unproven despite considerable effort.

Are all even integers greater than 4 Goldbach numbers?

Since four is the only even number greater than two that requires the even prime 2 in order to be written as the sum of two primes, another form of the statement of Goldbach’s conjecture is that all even integers greater than 4 are Goldbach numbers.

What is the modern version of the first and marginal conjecture?

A modern version of the first conjecture is: Every integer that can be written as the sum of two primes can also be written as the sum of as many primes as one wishes, until either all terms are two (if the integer is even) or one term is three and all other terms are two (if the integer is odd). A modern version of the marginal conjecture is: