- On November 17, 2003 Michael Shafer's computer found the 40th
known Mersenne prime, 2
^{20,996,011}-1! This number "weighs in" at a whopping 6,320,430 decimal digits! At that time, it was also the largest known prime number.Call this number

*p*. How did we know there must be prime numbers even larger than*p*? -
- Use the Pythagorean "triangular number" construction to
show that the sum of the integers from 1 to 17 is (17x18)/2.
- Show how this construction is really the same as Gauss'
argument:
1 + 2 + 3 + + 17 17 + 16 + 15 + + 1 _____________________________ 18 + 18 + 18 + + 18 (17 times).

- Use the Pythagorean "triangular number" construction to
show that the sum of the integers from 1 to 17 is (17x18)/2.