I need to test if a number is a prime number. Is there any program to test very large numbers like the biggest one with 17,425,170 digits ? I know about the Great Internet Mersenne Prime Search (GIMPS) project but I am not searching prime numbers. I just want to test them.

  • $\begingroup$ When you're asking about such a well-documented problem and you don't find the existing material on the Web accessible, it makes sense to point out in your question what part of e.g. the Wikipedia article on the topic you don't understand. Else people can only guess what your problem is and would effectively have to write another explanation all over again of something that's already been well explained many times. (If by "program" you mean concrete software, you'll find some in the "External Links" section of that article.) $\endgroup$ – joriki Sep 19 '15 at 11:08
  • $\begingroup$ I don't get which one is the fastest primality test. $\endgroup$ – vovahost Sep 19 '15 at 11:26
  • $\begingroup$ If I knew which one is the fastest I could try to implement that algorithm but the problem about how long the test will take to run on my computer still remains. Is it a matter of 1 year or 10 years ? $\endgroup$ – vovahost Sep 19 '15 at 11:36
  • $\begingroup$ Do you want to fing a record prime, or do you just want to find primes with, lets say, $20,000$ digits ? Do you want to find primes with a special form, or random primes ? $\endgroup$ – Peter Sep 19 '15 at 17:21
  • $\begingroup$ If you are content with a probable prime, you can get results with PARI/GP in a reasonable time, but it you want very large proven primes, they must have a special form. Otherwise it takes very long to find such a prime. $\endgroup$ – Peter Sep 19 '15 at 17:23

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