## Can you find one of the ‘lost’ primes?

The biggest prime number ever discovered is 17 million decimal digits long. Its predecessor, discovered in 2008 was 12 million digits long. Those are huge numbers, but there is also a huge gap between them.

In order to be efficient, the algorithms that have been developed to discover large primes will often leave large areas of unexplored territory in the number-space behind them: the “lost primes”.

We’re challenging you to use cloud computing to find one of those lost primes, and help to increase mathematical knowledge.

Prime Challenge

now

Have a look at this Deep Zoom which shows all the digits of the world’s largest known prime number…

## What are the Lost Primes?

When people search for very large prime numbers, they use algorithms which tend to leave areas of the number-space unexplored. A great example of this is the Mersenne Prime, which searches for new prime numbers using the algorithm 2^{p}-1 (where p is a known prime).

Let’s test it:

- We all know that 2
^{2}= 4. Then take one away from that leaving 3 and yippee – it’s a prime number. - 2
^{3}-1 = 7, yay! Another good result: a prime number. - 2
^{7}-1 = 127 – yippee! a prime number. - 2
^{11}-1 = 2047 – well, it was worth checking, but this is not a prime number. You can’t win ‘em all.. - 2
^{13}-1 = 8191 – it’s worked again!

So we’ve successfully discovered primes using this method, but we’ve also left rather a lot of holes in its wake. We’ve discovered 2, 3, 7, 127, and 8191. But even if we take the first few primes up to 100, this method has missed 5, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

As you can see, it’s easy to understand how there might be lots of “lost” primes.

## Cloud Computing and Prime Numbers

Most of the big prime discoveries have used many hundreds of thousands of computers over many years – it takes a lot of computing power to calculate a number that is 17 million digits long. This type of computing power was previously out of reach for casual observers. But cloud computing has changed that and we now all have access to a huge amount of computing power.

This challenge gives everyone the chance to discover new prime number by using cloud computing. We really aren’t expecting to get anywhere near close to the largest primes ever discovered, but we do expect to find many of the lost primes. The challenge will also highlight which architectures and configurations of cloud computing resources work best for this kind of task.

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