But what actually is the Riemann Hypothesis? It is a conjecture about the location of the non-trivial zeros of the Riemann Zeta function, it states that all the zeros should lie on the critical strip 0.5+it. "Oh yeah!", I hear you cry, now you get it, obviously. I will explain what this means properly later on in this post. But first I will state what it means. If true it implies a lot of things about the distribution of prime numbers, and as you may or may not know they are very irregular and very difficult to find as the numbers get very, very big.

To track back to my earlier point, what is the Riemann Zeta Function ( it is denoted as ζ(s), ζ being the Greek lower case from which z was derived)?

Where s is an imaginary number, a+ib. |

As you may or may not notice this is comprised of the prime numbers, this means that there is a sort of subliminal link between the natural numbers and the prime numbers. This showed that the prime numbers were not just positioned randomly and are not merely the building blocks to numbers but there is an actual link between them and the natural numbers.

The Riemann Zeta Function on its face doesn't look too difficult, I mean it is just an infinite sequence, even with a complex power you'd expect this to be possible and even pretty easy. But that is not the case at all, part of the reason is how sporadic complex exponents can be, and although it is not too difficult to find solutions (using a high powered computer thousands can be found each hour) it is incredibly, incredibly hard to find a proof for all the solutions.

The plot of the Riemann Zeta Function, the red line is the real part, the blue part is the imaginary part. |

Every mathematician worth his salt has had an encounter with the Riemann Hypothesis and it has withheld every single attempt thus far. The maths used to try and tackle the problem is so complex that entirely new branches of mathematics have been created to deal with it, this maths to laymen has literally nothing, at all, to do with the prime numbers. It is so complex and far away from the problem that it almost boggles mathematicians minds, but it consumes them, it is their passion and life.

Prime numbers are the passion for many and the Riemann Hypothesis is merely an extension of that, and hopefully it will be solved in my life time.

If you have caught the prime number bug I suggest you read the excellent book by Karl Sabbagh called Dr Riemann's Zeros.

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