The Guadalajara Reporter

Finding a prime number to test your computer

Prime numbers are those numbers divisible only by itself and one.  For centuries mathematicians calculated them hoping to make some kind of a breakthrough that might prove them to be useful.  A Mersenne prime is a prime number that is also all ones in binary (3 is 11 binary, 7 is 111, etc.)  Up until the 19th century, there was little use for either flavor of prime numbers, and calculating these numbers was a purely mathematical exercise until cryptographers discovered how to use them to create nearly unbreakable codes.

It was found that using two prime numbers multiplied together makes a much better encryption key than any random number, because the product has only three factors.  Large prime numbers (hundreds or thousands of places long) are exceedingly hard to factor and cryptographic keys derived from them are likewise computationally infeasible to crack.

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