20200513, 21:52  #12 
"Curtis"
Feb 2005
Riverside, CA
2^{2}×1,097 Posts 
You keep saying "calculating 2^{some 5digit number}". What calculation are you doing?
You don't need the decimal expansion to decide if it is prime. You also don't need to write your own software. So, what is it you want to do? I feel like you intend to find some primes, and then write (to disk? To screen? both?) out the decimal expansions of those primes. But you aren't even telling us what numbers you are checking. 2^50000 is obviously not prime; do you mean 2^50000 1, or 2^50000 +1, or something else entirely? You mentioned fermat and mersenne primes those have been checked to quite large values, and software is easily available if you wish to contribute to those searches. Why start over from scratch, which gives you no chance whatsoever to discover something previously unknown? 
20200514, 02:07  #13 
"Rashid Naimi"
Oct 2015
Remote to Here/There
1923_{10} Posts 
Look at the link in post number 6. It's a program that you can download for free and set up. It's a calculator which can calculate any number you give it instantly. You don't need to write your own program. There is no theoretical limit on how big a number you can give it. The only limitation is your computer's memory. Regardless you can instantly calculate numbers with millions of digit. Proving then prime can take very long time. Days, months, years....

20200514, 06:50  #14 
"murat"
May 2020
turkey
53 Posts 
okay . my method to calculate exponents of 2 is similar to used methods and it is slower than them . I am calculating all because maybe I catch a relation of them so I need a library
what did I do until now . I achive 3 method to check primes . one is for twin primes and it is well known . one is primes and sont have advantag to clasicap method . one for 6 x k  1 primes . in this method you dont use all primes until squareroot . but it cant reduce number of calculation. I worked on goldbach 4 ways for even numbers 2 ways to odd numbers I also calculatwd numbers until 10^7 but no one doesnt explain infinity I found a speciality of fibonacci numbers but I think it is known I am working two geometrical shape can be related with primes and some more I must look my papers I use simple maths for calculation thats all :) Last fiddled with by drmurat on 20200514 at 06:57 
20200514, 08:28  #15  
"murat"
May 2020
turkey
53 Posts 
Quote:


20200515, 18:39  #16  
"Sam"
Nov 2016
2^{2}·79 Posts 
Quote:
If a does not divide n, n is prime > a^n = a mod n > a^(n1) = 1 mod n ^{What happens when n is composite?} Last fiddled with by carpetpool on 20200515 at 18:39 

20200515, 18:59  #17  
"Curtis"
Feb 2005
Riverside, CA
2^{2}·1,097 Posts 
Quote:
The number 2^n may indeed be as large as those descriptions, but the exponent 'n' cannot. 2 raised to a thousandsofdigits number is not an item we contemplate for primality testing, ever. 

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