No 47

This doesn't continue or does it?

Prime numbers are notorious for producing apparent patterns that eventually fail...

3, 31, 331, 3331, 33331, 333331, 3333331 and 33333331 are all Prime numbers... now do the following calculation: 17 x 19607843 and be amazed.
In mathematics the symbol ! is called the factorial sign. Examples of its use are:
4! = 4 x 3 x 2 x 1 = 24 and 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Check the following calculations:

3! - 2! + 1! = 5

4! - 3! + 2! - 1! = 19

5! - 4! + 3! - 2! + 1! = 101

6! - 5! + 4! - 3! + 2! - 1! = 619

7! - 6! + 5! - 4! + 3! - 2! + 1! = 4421

9! - 8! + 6! - 5! + 4! - 3! + 2! - 1! = 35899

All these answers are Prime numbers. Now calculate the next value and compare it with 79 x 4139 and be amazed.
If you discover a prime number pattern that doesn't continue (or does it?) then we want to know.

If you have answers, discoveries, new questions etc to do with this Number Fact then...

E-mail us at madrascollege.maths@fife.gov.uk
...and we will publish them here.

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