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primenumbers@yahoogroups.com,

"WarrenS" <warren.wds@...> wrote:

> Wow!

> Allegedly Yitang Zhang proved there are infinitely many

> pairs of primes that are less than 70 million units apart:

>

> http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989

>

> The Zhang result is to be published in Annals of Maths and

> would seem an absolutely fantastic breakthrough.

That was my reaction.

> And Harald A. Helfgott gives a long proof every odd number N > 5

> is the sum of three primes (this was already long known to be true

> except for a computable finite set of possible exceptions):

>

> http://arxiv.org/abs/1305.2897

This is indeed cleaning up on previous breakthroughs,

but very welcome, nonetheless.

As Terence Tao had said, and I had here echoed:

> Busy day in number theory

Happily,

David