Breaking news about twin prime conjecture.

[caffeinemachine]

I don't know if this has already been posted. This article is about a possible proof of the twin prime conjecture. This is a breakthrough in the field of Number Theory.
First proof that infinitely many prime numbers come in pairs : Nature News & Comment

 

[Evgeny.Makarov]

From what I understood, this is not a proof of the Twin Prime Conjecture itself. The result states that there are infinitely many pairs of primes, but these primes are not twins, or siblings, or even cousins. They can be 70 million apart. In Russian, such relatives are called "seventh water on a kissel" (don't ask me why). But previously it was not known whether there is any finite number $n$ such that there are infinitely many pairs of primes at most $n$ apart. There is hope of reducing the 70 million number, but it is not clear how hard it would be to reduce it all the way to 2.

 

[mathmaniac1]

For me 70 million is still more like infinity.

 

[Ackbach]

For me 70 million is still more like infinity.

As one of my professors said, in relation to the cardinality of the Monster group, "It's cheating to call that finite."

 

[caffeinemachine]

From what I understood, this is not a proof of the Twin Prime Conjecture itself. The result states that there are infinitely many pairs of primes, but these primes are not twins, or siblings, or even cousins. They can be 70 million apart. In Russian, such relatives are called "seventh water on a kissel" (don't ask me why). But previously it was not known whether there is any finite number $n$ such that there are infinitely many pairs of primes at most $n$ apart. There is hope of reducing the 70 million number, but it is not clear how hard it would be to reduce it all the way to 2.

You are right. Although the title of the article says 'First Proof of TPC'

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I think 70 million is same as 2 for analysts.

 

[alyafey22]

I think 70 million is same as 2 for analysts.

Agreed

 

[TheBigBadBen]

For me 70 million is still more like infinity.

I can assure you that 70 million is still infinitely smaller than infinity.

 

[Fernando Revilla]

Also, we can assure that the infinite $\aleph_0$ is still infinitely smaller than the infinite $2^{\aleph_0}$. :)

 

[agentredlum]

Pick any infinite set with any cardinality greater than Aleph Null and call that infinite set S.

The Powerset of S has larger cardinality than S itself and therefore higher level of infinity. Repeat the process ad infinitim (what's going to stop you?) to see that the increasing levels of infinity are infinite.

For any given infinity there is always a higher infinity.

It is amazing what you can accomplish simply by asking your students to sit down.

:)