Simple arithmetic?
Goldenbach's conjecture states that any even number is the sum of two primes only. If we consider the theorem true, does this have any strong conjecture for the density of primes in a given partition? e.g. in a given interval/partition 2n-4n, how many primes must exist in the preceding partition/interval n-2n? ie there can't be zero primes in this interval?! Sorry about the lack of formal mathematical symbolism, but I lack any formal training and am still struggling with the formal propositions concerning the properties of simple integers- cheers!
Answers:
Because the number is even, say 2N, then there must be at least one prime between 1 and N and another prime between (N+1) and 2N because these are the 2 numbers that add together to give 2N. However, what if the number N is 2P for P a prime? Then, the two numbers that satisfy the Goldenbach conjecture are P and P.
So, either 2N = 2P for P a prime, therefore N is a prime
or 2N = P1 + P2 for P1<N and P2>N
Therefore, we conclude that for any even number 2N, there must exist at least 1 prime on the interval [N, 2N)
7 xx
Give me some of what you are on. LSD must have improved!
Though not related to Goldbach comjecture you can refer to the link beow to kow density of prime number
There would be a minimum of 2. This is a very good conjecture that I had not seen before.
Sorry, I can't be of enormous help here, it is beyond my math skills. But I did find the following link on wiki. It appears that you were misspelling his name so maybe if you google Goldbach's conjecture you will be able to get a more rigorous answer.
Good luck
who cares its poets day
Frankly my dear I don't giver a damn.
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Answers:
Because the number is even, say 2N, then there must be at least one prime between 1 and N and another prime between (N+1) and 2N because these are the 2 numbers that add together to give 2N. However, what if the number N is 2P for P a prime? Then, the two numbers that satisfy the Goldenbach conjecture are P and P.
So, either 2N = 2P for P a prime, therefore N is a prime
or 2N = P1 + P2 for P1<N and P2>N
Therefore, we conclude that for any even number 2N, there must exist at least 1 prime on the interval [N, 2N)
7 xx
Give me some of what you are on. LSD must have improved!
Though not related to Goldbach comjecture you can refer to the link beow to kow density of prime number
There would be a minimum of 2. This is a very good conjecture that I had not seen before.
Sorry, I can't be of enormous help here, it is beyond my math skills. But I did find the following link on wiki. It appears that you were misspelling his name so maybe if you google Goldbach's conjecture you will be able to get a more rigorous answer.
Good luck
who cares its poets day
Frankly my dear I don't giver a damn.
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