A Mersenne prime is a prime of the form 2^{P}-1. First Mersenne primes are 3, 7, 31, 127. Recently, researchers have discovered the two largest known Mersenne primes with 12,978,189 and 11,185,272 digits.
The larger number qualifies for a $100,000 research award. If you want to make some money, you can go for the 47th Mersenne prime. For more information, check out the webpage of GIMPS- Great Internet Mersenne Prime Search.
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