Where can I validate $300\ 000$ digit prime number is valid one?

Question

I recently found a different method to compute prime number in $\mathcal O(\log(\log n))$ complexity. At present, that logic working fine for $300$ digits prime number, which I found on websites.I need to validate whether that logic will be working fine for a higher number of digits. At present, I have computed a prime number of $300\ 000$ digits(but I am not sure whether this would be valid),

My questions are:

• Where can I find a prime number of higher digits i.e., more than $300\ 000$ digits?
• Where can I validate $300\ 000$ digit prime number is valid one?

Answer 1

From what you write I understand that you want to prove that your method is fine. It probably is if you checked up to 300, digits. But the only way to validate a method is by analysing it step by step and actually prove that it works. No matter how many digits you try, that will not be a proof that your method has no flaws.

Answer 2

Check it with a table of Mersenne primes (e.g. http://oeis.org/A000043) or use provable primes (e.g. Maurer's method, see Alg. 4.62 in the Handbook of Applied Cryptography).

Answer 3

Primo does this. It only runs on Linux, if you don't have one at home you can just create a virtual machine and run it as guest within your current OS. There are various tests that Primo can perform, please read the documentation on the website in order to adapt it to your special case.

Please note that it will take very long to certify that a $3\times10^{6}$-digit number is prime. If you want to test your method on large numbers, take a much smaller one to begin with, i.e., with about $10^{3}$ or $10^{4}$ digits.