prime numbers Watch

nityaaditya
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What's so weird about prime numbers?
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Manitude
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They don't (seem to) follow any patterns. At least that's the first thing that springs to mind.
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RainbowKiwi
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(Original post by Manitude)
They don't (seem to) follow any patterns. At least that's the first thing that springs to mind.
The dude's spamming tsr :lolwut:
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nityaaditya
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(Original post by RainbowKiwi)
The dude's spamming tsr :lolwut:
thanks for the answer and how the hell am i spamming huh?
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jsMath
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What is weird about prime numbers?
I will try to explain the concepts in the simplest form possible avoiding technicality at most parts.In short they are almost random by nature.

Consider a sequence of even numbers, you can easily see a pattern that generates an equation that governs the sequence in which you can guess and prove in many ways its 2n.
Where n = 0,1,2,3...

However when it comes to prime numbers this isn't the case.

Think about the prime numbers less than 10
2, 3,5, 7, can you conjunct or guess a pattern?
As you can see you have 4 prime number when counting less than 10.you might say it could be 2n+1. It seems a rational expression, but let's test it!
Let's assume that 1 is a prime number, this is debatable.

If n=1 then 2n+1 = 3

if n=2 then 2n+1 = 5

if n=3 then 2n+1 = 7

if n=4 then 2n+1 = 9 fails the test.

Another problem that 2 is a prime not achieved by the formula
how many primes are there from 10 to less than 20?

11, 13, 17, 19

again we have 4 prime numbers here but can't seem to find an equation.
Try to think of it just for the sake of understanding the concept in terms of arithmetic series or sequence.

As you can see if you keep going on and on there isn't a simple formula that describes the behavior of prime sequence.

A great mathematician Carl Friedruch Gauss manged to conjunct prime number theorem , by plotting a chart of range of prime numbers vs new prime number, in which he innovated a prime counting function, the function turned out to be the reciprocal of the natural logarithms.

So pi(n) – n/1n(n)

Guass wasn't able to prove his conjuncture, it took about another hundred years to prove his envision.
This form of behavior provides a margin of estimated error to accuracy.

if I was to mention every effort done to solve the problem of prime number weird random behavior, I will have to write several volumes, am trying to keep it short and as simple as possible.

Bernhard Riemann came up with a hypothesis famously known as the Riemann hypothesis implying the distribution of prime numbers. It took me 20 pages of hand writing and almost 6 hrs to prove his formula derived from the zeta function.

if you want to see how weird it is look at the following equation and try to solve it.

here is one way to express the result.



\pi ^{-\frac{s}{2}}\zeta (s)= \pi ^{-\frac{1+s}{2}} \Gamma (\frac{1-s}{2})\zeta(1-s))

you can also express the result in terms of sine and cosine.

if you can solve this expression where (s in complex plain) to prove or disporove Riemann hypothesis you can win a 1000000 dollars prize.

I don't know what level you are at Mr or Mrs, to analyse the concept in the complex world, but hopefully you got an idea; why primes are wierd or almost random by nature?

If you have any further question on this matter, do not hesitate to ask.

The wierdest thing here is that one can derive the formula but can't find a solution till now.
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Manitude
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(Original post by RainbowKiwi)
The dude's spamming tsr :lolwut:
I noticed after I posted that the OP was posting a lot of questions in a lot of topics. Some of them were moderately insightful and some were easily googleable.
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nityaaditya
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manitude are u siding me or against me i dont understand

and thanks for the answer it was helpful who ever wrote the huge answer
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TeeEm
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(Original post by jsMath)
What is weird about prime numbers?
I will try to explain the concepts in the simplest form possible avoiding technicality at most parts.In short they are almost random by nature.

Consider a sequence of even numbers, you can easily see a pattern that generates an equation that governs the sequence in which you can guess and prove in many ways its 2n.
Where n = 0,1,2,3...

However when it comes to prime numbers this isn't the case.

Think about the prime numbers less than 10
2, 3,5, 7, can you conjunct or guess a pattern?
As you can see you have 4 prime number when counting less than 10.you might say it could be 2n+1. It seems a rational expression, but let's test it!
Let's assume that 1 is a prime number, this is debatable.

If n=1 then 2n+1 = 3

if n=2 then 2n+1 = 5

if n=3 then 2n+1 = 7

if n=4 then 2n+1 = 9 fails the test.

Another problem that 2 is a prime not achieved by the formula
how many primes are there from 10 to less than 20?

11, 13, 17, 19

again we have 4 prime numbers here but can't seem to find an equation.
Try to think of it just for the sake of understanding the concept in terms of arithmetic series or sequence.

As you can see if you keep going on and on there isn't a simple formula that describes the behavior of prime sequence.

A great mathematician Carl Friedruch Gauss manged to conjunct prime number theorem , by plotting a chart of range of prime numbers vs new prime number, in which he innovated a prime counting function, the function turned out to be the reciprocal of the natural logarithms.

So pi(n) – n/1n(n)

Guass wasn't able to prove his conjuncture, it took about another hundred years to prove his envision.
This form of behavior provides a margin of estimated error to accuracy.

if I was to mention every effort done to solve the problem of prime number weird random behavior, I will have to write several volumes, am trying to keep it short and as simple as possible.

Bernhard Riemann came up with a hypothesis famously known as the Riemann hypothesis implying the distribution of prime numbers. It took me 20 pages of hand writing and almost 6 hrs to prove his formula derived from the zeta function.

if you want to see how weird it is look at the following equation and try to solve it.

here is one way to express the result.



\pi ^{-\frac{s}{2}}\zeta (s)= \pi ^{-\frac{1+s}{2}} \Gamma (\frac{1-s}{2})\zeta(1-s))

you can also express the result in terms of sine and cosine.

if you can solve this expression where (s in complex plain) to prove or disporove Riemann hypothesis you can win a 1000000 dollars prize.

I don't know what level you are at Mr or Mrs, to analyse the concept in the complex world, but hopefully you got an idea; why primes are wierd or almost random by nature?

If you have any further question on this matter, do not hesitate to ask.

The wierdest thing here is that one can derive the formula but can't find a solution till now.
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TeeEm
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#9
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Manitude and RainbowKiwi why aren't you in the chat forum?
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