How can I enter a larger exponent?

[evanh]

Originally Posted by petrw1

Prime95 is limited to 560M.
Results you see for larger exponents are using different software of which I have no experience. As well I believe those who are trying are using LL testing software on their GPUs.

But as several have said; you truly may not live to see it complete unless you have a super computer or very fast GPU.

Check out any of these that have LL as the Work Type and that have a completion date.
https://www.mersenne.org/assignments...&exp1=1&extf=1

I have come across these but I am curious what their benchmarks are... here are mine below..

I get it Prime95 has a tried and true method so why stray from it right? Have you ever seen the video on youtube of Richard Feynman discussing the difference between Mathematicians and Physicists? the whole video is good but the part I am referring to startes at about 5:40. https://www.youtube.com/watch?v=obCjODeoLVw He basically goes on to say that guessing the equation seems to be a good way to discover new things... essentially I would like to apply my personal method to finding prime numbers and testing those... I just have no way to test... womp womp womp .... guess I need to really learn programming now... :)

[retina]

Originally Posted by evanh

I have come across these but I am curious what their benchmarks are... here are mine below..

Those results don't apply to 1 billion digit exponents. There is no software in existence that can test such an enormous number. There is no computer in existence that can even store such an enormous number. Do you really know what you are asking for? Even in the best possible case of a base-2 one-billion-digit-exponent that is still something like 10^{332...<skip ~999,999,993 digits>...xxx}.

[evanh]

Originally Posted by retina

Those results don't apply to 1 billion digit exponents. There is no software in existence that can test such an enormous number. There is no computer in existence that can even store such an enormous number. Do you really know what you are asking for? Even in the best possible case of a base-2 one-billion-digit-exponent that is still something like 10^{332...<skip ~999,999,993 digits>...xxx}.

I think there is a miscommunication I am not referring to a billion digit exponent.... but a billion digit result

[science_man_88]

Originally Posted by evanh

I think there is a miscommunication I am not referring to a billion digit exponent.... but a billion digit result

That's still over 3 GB to store the number.

[evanh]

That is pretty cool, how did you come up with that storage size?

Also, is this a reason that the calculation could not be done? I have storage space, RAM.. and more importantly... time :)

[a1call]

Evan,
Have you looked into Pari-Gp.
It's isprime function is deterministic and one of the fastest off the shelf functions for primality testing. For general form primes you can use primo it has limited (but large) parallel processing capability. It can only run on 64 bit Linux machine and will require a few lifetimes to come up with certificates for very large numbers.
IMHO your best chance of proving your 1G dd integer prime is writing your own code using Lucas primally test and not LL test. You will have to write your own code make your own hardware (a PC won't do) and find all the prime factors of n-1 where n is your prime candidate. This could be trivial and virtually instantaneous (relatively speaking) if the C in your formula can be -1.
If you see a discussion about the number of atoms in the universe, you can just ignore them

[science_man_88]

Originally Posted by evanh

That is pretty cool, how did you come up with that storage size?

Also, is this a reason that the calculation could not be done? I have storage space, RAM.. and more importantly... time :)

okay my math is bit off,. It's all to do with logarithms. Also look up computational complexity.

[ET_]

Originally Posted by evanh

That is pretty cool, how did you come up with that storage size?

Also, is this a reason that the calculation could not be done? I have storage space, RAM.. and more importantly... time :)

You are Majoring in math and Physics... Consider learning a bit about computational complexity Such subject is all about how "hard" a calculation is, based on simple atomic operations. It also explain things like logarithmic, linear, polynomial and exponential time to reach a result (you should have learnt about asymptotics while studying Calculus I). Using such tools it becomes quite easy to define how long a computation will take, and how many bytes it will need to accomplish its goal.

And, yes, the answer to your last qustion lies on it. Unless you have petabytes of RAM and at least 85 years' time, you won't succeed.

[evanh]

Originally Posted by ET_

You are Majoring in math and Physics... Consider learning a bit about computational complexity Such subject is all about how "hard" a calculation is, based on simple atomic operations. It also explain things like logarithmic, linear, polynomial and exponential time to reach a result (you should have learnt about asymptotics while studying Calculus I). Using such tools it becomes quite easy to define how long a computation will take, and how many bytes it will need to accomplish its goal.

And, yes, the answer to your last qustion lies on it. Unless you have petabytes of RAM and at least 85 years' time, you won't succeed.

Yes I am familiar with asymptotics. I am basically a newborn in the world of computational anything... however, I am very capable of learning just about anything. I see your, and everyone else's, point regarding the amount of time it would take.

Perhaps I will try my method on 100,000,000 digit primes and if my probabilistic test within Maple comes up "true" then I can move forward from there.

Also, I guess I can start here>> https://en.wikipedia.org/wiki/Comput...plexity_theory
then move on to the textbooks referenced on that site.

[evanh]

currently working on a number close to this one, Maplesoft.. The only problem is that I do not have an estimated time to completion and no way to save my progress.

usually if the number is "false" it returns fairly quickly.. this one is taking its time so we shall see.

[VBCurtis]

Originally Posted by evanh

Perhaps I will try my method on 100,000,000 digit primes and if my probabilistic test within Maple comes up "true" then I can move forward from there.

Try 10,000 digits. Then try 100,000. Then consider how much longer the second case takes, extrapolate. Perhaps once you have a concept of how many lifetimes your goal will take, you can then explore the limits of the software you have available to you.