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Every odd integer larger than 1 is the sum of at most five primes

Terence Tao has uploaded to the arXiv a paper “Every odd number greater than 1 is the sum of at most five primes“, submitted to Mathematics of Computation. He says this result is:

in the spirit of (though significantly weaker than) the even Goldbach conjecture (every even natural number is the sum of at most two primes) and odd Goldbach conjecture (every odd natural number greater than 1 is the sum of at most three primes). It also improves on a result of Ramaré that every even natural number is the sum of at most six primes. This result had previously also been established by Kaniecki under the additional assumption of the Riemann hypothesis, so one can view the main result here as an unconditional version of Kaniecki’s result.

Interesting Esoterica Summation

I feel like it’s time to do another summary of my recent additions to the Interesting Esoterica collection.

A reminder of what it’s all about: every now and then I encounter a paper or a book or an article that grabs my interest but isn’t directly useful for anything. It might be about some niche sub-sub-subtopic I’ve never heard of, or it might talk about something old from a new angle, or it might just have a funny title. I put these things in my Interesting Esoterica collection on Mendeley.

In this post the titles are links to the original sources, and I try to add some interpretation or explanation of why I think each thing is interesting below the abstract.

Click here to continue reading Interesting Esoterica Summation on cp’s mathem-o-blog

A 17×17 4-colouring with no monochromatic rectangles

Described on The Math Less Traveled

Interesting Esoterica Summation

I’m going to try collecting additions to my Interesting Esoterica collection in let’s-say-weekly posts. I’ll link to each item, maybe paste its abstract, and write a sentence or two about it. Let’s see if it catches on. I’m not sure if I’ll have the will to do this regularly. I’m in a bit of a getting-things-done mood today.

As this is the first one, and I’ve added loads of stuff in January, for this first post I’m using everything  I’ve added since the New Year. Future posts shouldn’t be anywhere near as long.

I should explain what the Interesting Esoterica collection is about.

Click here to continue reading Interesting Esoterica Summation on cp’s mathem-o-blog

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