Project B11 Page 3 of 6

In one or two complete sentences, explain why every prime number is deficient. Be sure your entire explanation appears in the box below.

If n is any natural number, then 2ⁿ is almost perfect. Look at several examples of numbers of the form 2ⁿ and make a conjecture about the sum of their proper divisors. Be sure your entire conjecture appears in the box below.

For any natural number n, the sum of the proper divisors of 2 raised to the power n is

Euclid proved that 2^n-1(2ⁿ-1) produces a perfect number whenever 2ⁿ-1 is prime. Find the first four such perfect numbers.

n = 2^n-1(2ⁿ-1) =

n = 2^n-1(2ⁿ-1) =

n = 2^n-1(2ⁿ-1) =

n = 2^n-1(2ⁿ-1) =

Find another perfect number. Either use Euclid's idea or search any available resources.

When you are satisfied with your results, print this page and continue with the next.