Puzzle #3: 3×3 Grid

The numbers from 1 to 9 are arranged in a 3×3 grid:
a    b    c
d    e    f
g    h    i
subject to:

  1. The corner numbers are all odd.
  2. One diagonal sums to 20, and its numbers ascend from left to right.
  3. All of the numbers in one column are squares.
  4. One row sums to 20, and its numbers ascend from left to right.
  5. All of the numbers in one column are primes.
  6. In one row, one of the numbers is the product of the other two.
  7. One column’s numbers are consecutive (though not necessarily in order).
  8. a = 3.

What are the values of a through i?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, June 26, 2013 at noon Pacific Time. I will post the answer shortly after.