Largest Prime Number Found: 17,425,170 Digits Long

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The largest prime number yet has been discovered — and it's 17,425,170 digits long. The new prime number crushes the last one discovered in 2008, which was a paltry 12,978,189 digits long.

The number — 2 raised to the 57,885,161 power minus 1 (257885161 -1) — was discovered by University of Central Missouri mathematician Curtis Cooper as part of a giant network of volunteer computers devoted to finding primes, . . . .
http://news.yahoo.com/largest-prime-number-discovered-165757465.html
 
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As someone said before (Appel & Haken?): now the burden lies on proving that the algorithm is correct. :)
 
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.