Oh right - the largest one found so far...
I vote for infinity -1 as the largest prime.
What would Cantor say?
As someone said before (Appel & Haken?): now the burden lies on proving that the algorithm is correct. :)
largest KNOWN prime number.
Indeed already the Greek mathematician Euclid of Alexandria (fl. 300 BC) proved in his Elements, Book IX, Proposition 20 that the number of primes is infinite wherefore there cannot be the largest one.
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