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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: 26972593-1. 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 38th Known Mersenne Prime by George Woltman, pages 367-370 (which you may have to find in the library of your local university).

They are called 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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Primes, Factors and Divisibility