Terence Tao has posted a new paper on the arXiv giving a proof that all odd integers greater than 1 can be written as the sum of at most 5 primes. This was proven before, on the assumption of the Riemann Hypothesis, but he has removed the need this assumption. The key work in the title is **ALL**; previous work has shown that any **LARGE ENOUGH** integer can be written as the sum of at most three primes.

This is a pretty big step forward I think. For details, see Terence’s blog and the paper itself.

Happy 2012,

Tom

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