April 2, 2013

New Largest Prime Number Discovered

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With 17,425,170 digits, the newly discovered largest prime number exceeds most people’s imaginative capabilities. Far surpassing the previous record, a number over 12,000,000 digits, this new number is part of the perpetual quest for newer and larger prime numbers. The discoverer, Curtis Cooper, is no stranger to the search for prime numbers. This is his third discovery.

But what’s the point? Why find impossibly large prime numbers? It isn’t as if the organization searching for it, the Great Internet Marsenne Prime Search, offers significant compensation — $3,000 for each number found. Confirming the number to be a true prime alone took 39 days, never mind the time it took to calculate and find it in the first place.

According to Prof. Ravi Ramakrishna, Mathematics, “large prime numbers are used to make encryption algorithms more secure.” Large prime numbers end up being used as cryptogram-like keys to make access to sensitive data extremely difficult for outside people. The RSA algorithm, named after its creators, Rivest, Shamir and Adleman, utilizes large prime numbers in this manner.

According to Ramakrishna, the RSA algorithm relies on the fact that it is relatively easy to discover large prime numbers but much harder to factor larger numbers into primes. That is, a computer can potentially use less computation to figure out the next highest prime number than to try to factor down an equally long number to its primes. The algorithm is most commonly used in credit card encryption over the Internet.

Despite the practical application of large prime numbers, this new 17,000,000 digit one will probably be tucked away for quite some time. Encryption does not currently require the use of such big prime numbers.

“The scale of ‘big’ for those purposes is nowhere near that of this latest prime. A few hundred (or maybe thousand) digits suffices for these purposes,” Ramakrishna said. A number of that magnitude will likely not be needed for at least another next century. Yet, quantum computing is an expanding field. There may be a use for the number that we are simply not yet aware of. For now, the search for the next largest prime number continues.

With a new largest prime number being recorded every year, it may seem to be a pointless journey with no true ending. So why do people still do it?

According to Ramakrishna, “it’s the same reason we try to run a faster mile, climb a higher mountain, fly a plane faster — to see if we can!”

Original Author: Yvonne Huang