# Prime Generating Function

Today morning i was thinking about functions, i had it that if someone can design a prime generating function we can solve how prime numbers are distributed in the real plane. I mean if you look at functions in a very passive way, its like you are getting a desired output for a given input, so if someone can create a prime generating equation , we can actually solve the distribution of prime numbers.

Note by Karthik.Ps Sharma
5 years, 2 months ago

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\boxed{123} $$\boxed{123}$$

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I was also thinking the same way before, but then I realized that's very impossible as if the prime factors weren't usually in patterns. And if possible, we may just achieve an accurate result in small quantities but not in astounding numbers. ~

- 5 years, 2 months ago

the distribution is extremely hard to predict. Even a trillion consecutive composites do exist :D Proven using Chinese reminder theorem. It looks quite closely packed in the beginning, but it later becomes more and more sparse

- 5 years, 2 months ago

In fact, there can be arbitrary many consecutive composite

- 5 years, 2 months ago

Consider n! +2, n! + 3, ...n!+n, which are all composite, and represent n-1 consecutive composites

- 5 years, 2 months ago

Yes , but this a conjecture, nobody knows the distribution of prime numbers !

- 5 years, 2 months ago