Technology

# The Record For The World's Largest Prime Number Has Been Broken Again

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While most of the world was enjoying a Christmas-New Year break, computers at the Great Internet Mersenne Prime Search (GIMPS) were hard at work, and the result was the discovery of the largest known prime number, 277,232,971-1, on Boxing Day. The computers may not care, but for their operators, Christmas came just a day late.

We apologize, but we will not be publishing the number in full, as it is more than 23 million digits long, and a zipped text file of all of them is 10 Megabytes. Although it is a little under two years since the previous record, what was once a quite frequent event has become more of a rarity, and therefore worth noting. In the first eight years of the millennial, the record for the largest prime was broken seven times, but in the past nine years, only three record-breakers have been added.

The latest prime is so large it took six days for verification to occur. Once this happened, GIMPS announced in a media release that, as well as being the largest yet discovered, the new prime is the 50th known Mersenne prime. This means that it takes the form of 2P-1, where P is also a prime number. Familiar Mersenne primes are 31 (25-1) and 127 (27-1). Mersenne primes set number theorists' hearts aflutter because they can be used to generate “perfect numbers”, those whose factors add up to their value. For example, aside from itself, 28's factors are 1, 2, 4, 7, and 14, which together equal 28.

Although Euclid proved that if 2P-1 is prime, then 2P-1*(2P-1) is a perfect number in 350 BC, the French monk Marin Mersenne was honored with the name for his conjecture of which prime numbers could be used for P to produce larger primes. Although written in the early 17th Century, the conjecture took 300 years to prove. Meanwhile, Euler also got in on the act, proving that all even perfect numbers are formed this way.

Some may wonder if this quest for ever larger numbers is just a waste of good computing power, but there is more to the search for large primes than a mathematical equivalent of trying to climb ever-higher mountains. Finding ways to test for primeness among such epically large numbers has pushed computing to its limits, producing spin-offs in the same way that the space race has given us new technologies. Moreover, an understanding of prime numbers has been important for cryptography, and uncovering bigger ones helps us test theories on their distribution that may one day be useful.

GIMPS uses donated processing power to do its searching, and awarded electrical engineer Jonathan Pace \$3,000 for providing online access to the computer on which the discovery was made.

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Technology
• record,

• cryptography,

• prime number,

• Mersenne prime