# Count On

## Explorer

#### The Largest Prime?

We have already looked at prime numbers - those numbers whose only factors are themselves and 1 - and found some tips and shortcuts for testing if a number is prime.

There are *infinitely many prime numbers*, so our list of prime numbers will continue to grow without ever coming to an end.

However, the largest number *known to be prime* is a continual challenge and changes as computers get faster and faster and as more shortcut tests are invented by mathematicians.

On June 1, 1999, the latest *largest known prime number* was found - a number so large that it has 2,098,960 digits: 2^{6972593}-1. It took Nayan Hajratwala 111 days running part-time on a 350 MHz Pentium II computer and the result was then verified by three different computers using different software.

You can read more about it in *The Fibonacci Quarterly*, volume 37, November 1999, in an article entitled **On the Discovery of the 38 ^{th} Known Mersenne Prime** by George Woltman, pages 367-370 (which you may have to find in the library of your local university).

**prime numbers**because...

*...every other number can be made from multiples of prime numbers in essentially one way only:*eg: 4 = 2x2; 6 = 2x3; 8 = 2x2x2; 9 = 3x3; 10 = 2x5; 12 = 2x2x3;

If 1 was included as a prime number, then we can include as many "1" factors as we wanted and there would be many ways to write each number as a product of primes. It is mainly for this reason that 1 is not called a prime number.

See also more on *record-breaking prime numbers*.

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