Table of Contents
Has the Goldbach conjecture been proven?
The Goldbach conjecture states that every even integer is the sum of two primes. This conjecture was proposed in 1742 and, despite being obviously true, has remained unproven.
Who Solved Goldbach conjecture?
The best known result currently stems from the proof of the weak Goldbach conjecture by Harald Helfgott, which directly implies that every even number n ≥ 4 is the sum of at most 4 primes.
What is a Goldbach number?
A Goldbach number is a positive even integer that can be expressed as the sum of two odd primes. Note: All even integer numbers greater than 4 are Goldbach numbers. Example: 6 = 3 + 3.
Are there an infinite number of twin primes?
“Twin primes” are primes that are two steps apart from each other on that line: 3 and 5, 5 and 7, 29 and 31, 137 and 139, and so on. The twin prime conjecture states that there are infinitely many twin primes, and that you’ll keep encountering them no matter how far down the number line you go.
Where does Helfgott’s proof of Goldbach’s conjecture come from?
Helfgott’s proof covers both versions of the conjecture. Like the other formulation, this one also immediately follows from Goldbach’s strong conjecture. The conjecture originated in correspondence between Christian Goldbach and Leonhard Euler.
Is the ternary Goldbach conjecture true or false?
The present paper proves this conjecture. Both the ternary Goldbach conjecture and the binary, or strong, Goldbach conjecture had their origin in an exchange of letters between Euler and Goldbach in 1742. We will follow an approach based on the circle method, the large sieve and exponential sums.
When did Hardy and Littlewood prove the weak Goldbach conjecture?
In 1923, Hardy and Littlewood showed that, assuming the generalized Riemann hypothesis, the weak Goldbach conjecture is true for all sufficiently large odd numbers.
Is the Goldbach conjecture true for all prime numbers?
All prime numbers greater than 2 are odd numbers, however since the sum of two odd numbers is always even, then it is possible that Goldbach’s conjecture is true. Further more, the set of prime numbers is a subset of the odd integers, therefore, it is plausible for Goldbach’s conjecture to be true.