# Riemann Hypothesis implies Odd Number is Sum of at most 5 Primes

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## Contents

## Theorem

Let the truth of the Riemann Hypothesis be assumed.

Let $n$ be an odd integer.

Then $n$ is the sum of at most $5$ primes.

## Proof

## Historical Note

When this result was cited by David Wells in the $1997$ edition of *Curious and Interesting Numbers, 2nd ed.*, this was the limit of knowledge.

However, Terence Tao has since come up with a proof of this result which does not require the Riemann Hypothesis.

## Sources

- 1995: Leszek Kaniecki:
*On Šnirelman's constant under the Riemann hypothesis*(*Acta Arith.***Vol. 72**,*no. 4*: 361 – 374)

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $5$