Prime Numbers discovered through geometric representation

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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Comments

Not once here have you used any form of analytic geometry; I think you can do away with all the pictures. What you have here is a possible sieve algorithm that may involve some form of modular arithmetic. It looks less efficient than the common Sieve of Eratosthenes, so maybe you will need to improve on it; I am always interested in any sieve method that churns out prime numbers using classical computing methods, rather than the quantum computing methods, e.g. Shor's algorithm.

A Former Brilliant Member - 2 years, 6 months ago

Hello Genady, you're right in part, in fact I thought that the Caresian representation was part of the analytic geometry in reality it it is simply a method of geometric representation, so I'll correct the article accordingly. What we have here is an algorithm suitable for sifting numbers looking for prime numbers, to what I know there are infact no other methods to find prime numbers, as to the efficiency I can not calculate it even if in another article (https://brilliant.org/discussions/thread/linear-parametric-equation-for-primality-test/) I given some useful reference,anyway it is not a problem for me not having to challenge RSA, what I wanted to show is the beauty of this representation that is able to suggest such a method regardless of the definition of prime numbers and sieve. The utility, if anything, is only educational. Thanks anyway to have commented on the article. best regards Silvio Gabbianelli

Silvio Gabbianelli - 2 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$