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The QUEST for the Largest Prime

The QUEST for the Largest Prime. Mersenne Prime Numbers. Prime Number. A number divisible by only 1 and itself. Eg. 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,…. Mersenne Primes.

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The QUEST for the Largest Prime

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  1. The QUEST for theLargest Prime Mersenne Prime Numbers

  2. Prime Number • A number divisible by only 1 and itself. • Eg. 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,…

  3. Mersenne Primes The easiest way to find some of the prime numbers is by calculating: 2n-1 Problem: Not all are prime!

  4. Edouard Lucas In the 1870's the French mathematician Edouard Lucas was the first person to find a way to test if a number was prime without dividing it by all the primes smaller than its square root.

  5. 225,964,951-1 The largest known prime has just been discovered, not by a university academic, but by a German eye surgeon, Dr Martin Nowak February 18th 2005 … 50 days of calculations to test if this number was prime

  6. The 42nd known Mersenne prime The prime discovered by Nowack has 7,816,230 digits - over half a million digits more than the previous largest known prime number.

  7. No Prize Money But this is still short well of the ten million digits needed to claim the $100,000 prize offered by the Electronic Frontier Foundation.

  8. Great Internet Mersenne Prime Search(GIMPS) GIMPS uses the combined power of thousands of otherwise idle computers to churn through the calculations necessary to test whether Mersenne numbers are prime.

  9. GIMPS Though this program has been checked many times, the probability that some software or hardware bug may lead to a false positive - the program says that the Mersenne number is prime though it is composite - is very low but not null."http://www.plus.maths.org.uk/latestnews/jan-apr05/mersenne42/index.html

  10. So, the search continues… • Is this number really prime? • What is the next prime number?

  11. How is this useful? • Almost all of the new methods for cryptography depend heavily on prime numbers

  12. How is this useful? • Every time you use your credit card on the internet, your account is kept secret from hackers thanks to the power of prime numbers.

  13. How is this useful? • Each e-business chooses two big primes, p and q, which they keep secret. The product of these primes, N=pxq, is made public.

  14. How is this useful? • A calculation using N encrypts your credit card, but the only way to undo the calculation and decrypt the secret message is to know the secret primes p and q.

  15. How is this useful? • Cracking codes is the same as cracking the public number N into its prime building blocks. http://plus.maths.org/issue26/features/sautoy/

  16. How is this useful? • The two numbers, by the way, usually are 100 digits long or so, so factoring the product might require centuries on a large computer.

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