It was proven by Euclid that there are infinitely many prime numbers; thus, there is always a prime greater than the largest known prime. Many mathematicians and hobbyists search for large prime numbers. There are several prizes offered by the Electronic Frontier Foundation for record primes.
The fast Fourier transform implementation of the Lucas–Lehmer primality test for Mersenne numbers is fast compared to other known primality tests for other kinds of numbers. Due in part to this and to the historical interest in Mersenne primes, many of the largest known primes are Mersenne primes. As of June 2009 the nine largest known primes are Mersenne primes, while the tenth is the largest non-Mersenne prime. The last 14 record primes were Mersenne primes. Before that was a single non-Mersenne (improving the record by merely 37 digits in 1989), and 17 more Mersenne primes going back to 1952.
The use of electronic computers has accelerated the discoveries and found all records since 1951. The record passed one million digits in 1999, earning a $50,000 prize. In 2008 the record passed ten million digits, earning a $100,000 prize. Additional prizes are being offered for the first prime number found with at least one hundred million digits and the first with at least one billion digits.
This comment has been removed by the author.
ReplyDelete