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

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?
• A method with this complexity would be sensational! Is $\log(\log(n))$ actually the complexity of the method ? Commented Apr 4, 2018 at 13:13
• With PFGW , you can check your number Commented Apr 4, 2018 at 13:14
• Find a new prime of the form given in this question : math.stackexchange.com/questions/2635516/… Commented Apr 4, 2018 at 13:23
• I hate to sound overly skeptical, but just printing $n$ out has complexity $O(\log n)$. How is your algorithm outputting the candidate prime numbers? Commented Apr 4, 2018 at 13:45
• Oh, it's actually not clear to me whether you claim to have an algorithm that produces large primes, or whether the algorithm tests a given integer for primeness. Could you please clarify? Commented Apr 4, 2018 at 13:49

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.