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Mollet1955
- 9
- 0
if u have 3 primes: x,y,z
then prove its sum m=x+y+z is unique ? Thank you
then prove its sum m=x+y+z is unique ? Thank you
matt grime said:It's possible to find infinitely many counter examples, and there is a number less than 20 that is the sum of two primes in two different ways.
Tide said:Yes, but the question concerns three primes!
shmoe said:So add the same prime to both pairs.
I think that by other you have to find three totally different primes.Mollet1955 said:Oh I stated probme incorectly,
let x,y,z be primes, m=x+y+z
Can u find other three primes that can sum to get m ? m can be any number.
The concept of "Proving the Uniqueness of the Sum of 3 Primes" refers to the mathematical problem of determining whether a given number can be expressed as the sum of three prime numbers in only one way. This problem is also known as the Goldbach conjecture.
Proving the uniqueness of the sum of 3 primes is important because it helps to better understand the distribution of prime numbers and their relationships with each other. It also has practical applications in cryptography and number theory.
While the Goldbach conjecture has not been formally proven, there have been significant developments in this area. In 2013, a team of mathematicians used computers to verify the conjecture for all even numbers up to 4 x 10^18. However, there is still no proof for all odd numbers.
One of the main challenges in proving the uniqueness of the sum of 3 primes is the lack of a clear and precise definition of what constitutes a "prime number". Additionally, there are an infinite number of prime numbers, making it difficult to test all possible combinations.
If the uniqueness of the sum of 3 primes is proven, it could lead to a better understanding of the distribution of prime numbers and potentially help in solving other mathematical problems. It could also have practical applications in fields such as cryptography and data encryption.