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mathnerd15
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mathnerd15 said:so there is no total vacuum in the distribution of prime numbers, the density of twin primes never decreases below a certain value, twin primes are separated by less than 70 million at the most?
I'm excited to see the proof!
mathnerd15 said:what would reducing it to 2 mean?
The result is “astounding,” said Daniel Goldston, a number theorist at San Jose State University. “It’s one of those problems you weren’t sure people would ever be able to solve.”
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“This work is a game changer, and sometimes after a new proof, what had previously appeared to be much harder turns out to be just a tiny extension,” he [Granville] said. “For now, we need to study the paper and see what’s what.”
The Twin Primes Conjecture is a hypothesis in mathematics that states there are infinitely many pairs of prime numbers that have a difference of 2. For example, 41 and 43 are twin primes because they are both prime numbers and their difference is 2.
No, the Twin Primes Conjecture has not been proven. It is still an unsolved problem in mathematics.
In 2013, mathematicians Yitang Zhang and James Maynard made significant progress towards proving the Twin Primes Conjecture by showing that there are infinitely many prime pairs that are at most 70 million apart. However, the conjecture is still not fully solved.
The Twin Primes Conjecture is important because it is a fundamental problem in number theory and has connections to other areas of mathematics. Its proof would also have implications in cryptography and computer science.
Solving the Twin Primes Conjecture would not only answer a long-standing question in mathematics, but it would also contribute to a better understanding of prime numbers and their distribution. It would also open up the possibility for further research and advancements in the field of number theory.