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4=2+2, 6=3+3. Are there any other cases where an even number of the form 2p, where p is a prime, cannot be represented as the sum of two different primes?
mathman said:4=2+2, 6=3+3. Are there any other cases where an even number of the form 2p, where p is a prime, cannot be represented as the sum of two different primes?
The Goldbach conjecture variation is a variation of the original Goldbach conjecture, which states that every even integer greater than 2 can be expressed as the sum of two prime numbers. The variation includes an additional constraint that the two prime numbers must also be consecutive.
No, the Goldbach conjecture variation has not been proven. It is still an unsolved problem in mathematics. However, the original Goldbach conjecture has been verified for all even integers up to 4 x 10^18.
If the Goldbach conjecture variation is proven to be true, it would have significant implications in the field of number theory. It could potentially lead to a better understanding of the distribution of prime numbers and provide insights into other unsolved problems in mathematics.
Many different approaches have been used to try and solve the Goldbach conjecture variation, including computer simulations, probabilistic methods, and analytical techniques. Some mathematicians have also studied the original Goldbach conjecture in an attempt to gain insight into the variation.
The Goldbach conjecture variation is considered a difficult problem because it involves both prime numbers and consecutive numbers, which are both complex concepts in mathematics. Additionally, the problem has been studied for centuries without a solution, making it one of the most famous and intriguing unsolved problems in mathematics.