MAT 336 Stony Brook University Spring 2004

15-minute Quiz, March 5, 2004

1. 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?

    

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

   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).