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Is there a quick way to determine if this is a prime number?


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anyways I admit I learned a lot from this thread too. Can anyone suggest good math books for advance learnings. For masterals or doctorate degree?

Well, I recently bought a book called Masters Math: Calculus. There is a whole "series" of them ranging from Pre-Algebra to Calculus and I think more.

 

http://www.amazon.com/Master-Math-Debra-Anne-Ross/dp/1598639862

 

I think this is the book. The cover doesn't look the same as mine, but I'll see if I can find mine online and then post it.

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Well, I recently bought a book called Masters Math: Calculus. There is a whole "series" of them ranging from Pre-Algebra to Calculus and I think more.

 

http://www.amazon.com/Master-Math-Debra-Anne-Ross/dp/1598639862

 

I think this is the book. The cover doesn't look the same as mine, but I'll see if I can find mine online and then post it.

 

Thanks very much

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  • 2 months later...

Bumping this slightly dormant thread to share the below. There is a quick way to determine if a number is prime.

 

Quick? Perhaps with very small primes..

For computer it's completely not practical.

You don't want to solve unknown power equation on computer ever!

Unity+ wanted to check prime that has ~77 millions decimal digits...

Edited by Sensei
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Quick? Perhaps with very small primes..

For computer it's completely not practical.

You don't want to solve unknown power equation on computer ever!

Unity+ wanted to check prime that has ~77 millions decimal digits...

There may be ways to decrease the time it takes to run such a test, but there might not be.

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Quick? Perhaps with very small primes..

For computer it's completely not practical.

You don't want to solve unknown power equation on computer ever!

Unity+ wanted to check prime that has ~77 millions decimal digits...

 

I am not sure that is completely correct - it is definitely true in real world terms but...in theoretical terms the faster algorithms (which can be soft-O (log n)^4 if you are looking at Rabin-Miller) are not shown to certain yet, they rely still on unproven but very very likely assumptions. The Agrawal Kayal Saxena presented above is very much slower at soft-O (log n)^7.5. This has been improved from initially at soft-O (log n)^12 - and a variant is now at soft-O (log n)^6. For your guidance I cannot be sure how to get big O with a tilde above - so I have called it soft-O

 

Much the fastest are probabilistic - which are probably good enough cos the probability grows exponentially with each iteration. The next fastest are deterministic but rely on Reimann. The fastest that is deterministic and proven is basically that shown above.

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Bumping this slightly dormant thread to share the below. There is a quick way to determine if a number is prime.

 

 

 

The above is based on this paper: http://www.cse.iitk.ac.in/users/manindra/algebra/primality_v6.pdf

I did something interesting with the equation that they provided. I took the derivative of the equation and got the following:

 

om8h.png

 

The interesting thing is if you solve for x when the equation is equal to 0 if the number p is odd then you will always have one solution that is real(which is 1/2) while if it is even then it will only have complex solutions(I detect the Riemann Hypothesis in this equation).

 

This might lead down an interesting path.

Edited by Unity+
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I did something interesting with the equation that they provided. I took the derivative of the equation and got the following:

 

om8h.png

 

The interesting thing is if you solve for x when the equation is equal to 0 if the number p is odd then you will always have one solution that is real(which is 1/2) while if it is even then it will only have complex solutions(I detect the Riemann Hypothesis in this equation).

 

This might lead down an interesting path.

 

Just off the top of my head isn't it true that if that fact (you will always have one solution that is real(which is 1/2) while if it is even then it will only have complex solutions) is true of the derivative it must also be true of original.

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Just off the top of my head isn't it true that if that fact (you will always have one solution that is real(which is 1/2) while if it is even then it will only have complex solutions) is true of the derivative it must also be true of original.

I tried this out with one odd number: (x-1)^(3) - (x^3 - 1)

 

And the solutions are 0 and 1.

 

And the derivative will not always have the same solution as the original equation, but can in particular cases if I remember correctly.

Edited by Unity+
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I did something interesting with the equation that they provided. I took the derivative of the equation and got the following:

<...>

This might lead down an interesting path.

Glad it gave you some fresh insights. Good luck with the exploration.
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The more I look into this, the more interesting it gets.

 

im89.png

 

[math]-1>s>1[/math]

 

This function seems to bring about a similar graph as the Zeta function of the Riemann Hypothesis, but having the complex part becoming the real part of the function.

 

k35h.png

 

800px-RiemannCriticalLine.svg.png

 

In this function, the real solution for an even number s is determined by k as well, where [math]\mathbb{R}_{s}=k\frac{1}{2}[/math].

Edited by Unity+
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