The Goldbach conjecture is a famous unsolved problem in number theory that states every even integer greater than 2 can be expressed as the sum of two prime numbers.
The Goldbach conjecture has been a subject of interest for mathematicians for over 270 years. Its proof would provide insights into fundamental properties of prime numbers and contribute to our understanding of number theory.
If the Goldbach conjecture is proven, it would have a significant impact on the field of mathematics. It would also have practical applications in cryptography and computer security, as prime numbers are used in encryption algorithms.
If the Goldbach conjecture is disproven, it would mean that there are even numbers that cannot be expressed as the sum of two prime numbers. This would have major implications for number theory and could potentially lead to new mathematical discoveries.
The Goldbach conjecture remains an unsolved problem in mathematics. While it has been verified for all even numbers up to 4 x 10^18, a general proof or disproof has not yet been found. It is still considered one of the most challenging problems in number theory.