# Primality of a number of more than 50k digits

With modern tecnology is it possible to prove the primality of a number of more than 50k digits?

Obviously not a prime for which specific methods for testing primality are known like Mersenne primes.

• A Google search returned ellipsa.eu/public/primo/primo.html, which as of 2 years ago, in the last update, worked up to 50,000 digits. See also google.com/… Feb 8 at 8:43
• "possible", yes, for any number of digits that fits your machine, if you are patient enough. The question is a bit vague - we would expect you have read the literature on primality tests. So why "50k"? What do you know about the question already? Feb 8 at 9:19
• @ChrisWuthrich The number 50k might come from the fact that primo currently has (if I understand correctly) a hard-coded limit of 50k digits. Feb 8 at 10:31

Yes, it is possible, but it is close to the boundary of what is reasonable. See for instance this software that was recently used by Andreas Enge to prove the primality of $$10^{50000}+65859$$. It took 100 days of real time and 71 years of CPU time. The certificate can be verified in 4 hours with 128 cores.
• @BogdanGrechuk For instance the Pari/GP function ispseudoprime implements a version of the BPSW primality test, for which infinitely many pseudoprimes (composites that pass the test) are conjectured to exist but none is known. On the above example, it terminates in 15 minutes on a single core. Feb 8 at 19:44