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.
When I prepare for the Math/Maths Podcast I make some notes on each story so I have quick access to the key information when talking to Samuel Hansen. As an experiment, I have tried to tidy these up and place them here in my Math/Maths notebook.
Math/Maths Podcast: Peter Rowlett in the UK talks to Samuel Hansen in the US about news & current affairs.
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Monday, 13 February 2012
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:
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