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clearwater304
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For instance, the largest known prime number has nearly 13 million decimal digits. Would any normal computer be able to calculate this?
Awsome. I know when I took java a few years ago a lot of software would only store numbers up to a certain number of digits
clearwater304 said:Is there a way I can run mathematica remotely on their server.
I'm don't think that you meant this, but it should be reiterated that one does not ever need to find a factor of a number to prove that it's composite, even for extraordinarily large numbers.phyzguy said:What are you trying to do? Calculating a number like this is much, much faster than proving that it is prime. Encryption algorithms rely on the fact that multiplying two large primes to generate a large composite is much (much) faster than extracting these two primes from the resulting composite.
Solving 10^13000000=2^x gives x~40000000, which means it will take about 40 million bits to represent the number, which would be 5 million bytes. Since most computers have on the order of billions of bytes (gigabytes) the memory isn't the problem. The problem is the computation.clearwater304 said:Is there a way I can run mathematica remotely on their server. If I try to do a primality test on a very large number on my notebook it gives me a recursive error. I suppose this is due to the fact that it ran out of memory and I only have 4gb on my notebook.
Good luck with that. You might want to look at some other the existing ones first. The AKS primality test is the best known primality test.clearwater304 said:Mathematica seems to be the way to go, now I just have to create a customized primality test so it doesn't take a year to prove.
You do it you want your algorithm to be anywhere near efficient. EDIT: Never mind, I was wrong. I was presuming you were referring to the Wilson test, but I just remembered the quadratic residue test, which is a very efficient way to eliminate a lot of composite numbers without finding a factor.Feryll said:I'm don't think that you meant this, but it should be reiterated that one does not ever need to find a factor of a number to prove that it's composite, even for extraordinarily large numbers.
GMP, a C and C++ library, can handle arbitrarily large numbers and is very heavily optimized. So can Java's BigInteger, but I don't know how optimized it is.clearwater304 said:For instance, the largest known prime number has nearly 13 million decimal digits. Would any normal computer be able to calculate this?
The best software to calculate very large numbers is typically a high-performance computing (HPC) program that is specifically designed for handling large calculations quickly and accurately. Examples of HPC software include MATLAB, Mathematica, and Maple.
No, regular calculators and spreadsheets are not designed to handle extremely large numbers. They typically have a limited number of digits they can display and cannot handle numbers with many decimal places. Using HPC software is necessary for accurate calculations with very large numbers.
HPC software uses advanced algorithms and specialized data structures to efficiently handle large numbers. This allows for faster calculations and greater accuracy compared to regular software. HPC software also has the ability to work with multi-core processors and parallel computing, which further speeds up the calculation process.
Yes, there are some free and open-source options for HPC software, such as GNU Octave and Scilab. However, these may not have as many features and capabilities as paid software, so it is important to research and compare different options to find the best fit for your needs.
While HPC software is specifically designed for handling very large numbers, there is still a limit to the size of numbers it can handle. This limit is typically determined by the amount of memory and processing power available on the computer. However, HPC software can handle numbers with many more digits than regular software, making it the best option for calculating very large numbers.