MATH 380 Assignment #9

Goldbach's Conjecture is the assertion that every even number greater than or equal to four can be written as the sum of two (not necessarily different) prime numbers. For example, 4=2+2, 6=3+3, 8=5+3, 10=7+3 (and 10=5+5), 12=7+5, and so on. It's a conjecture rather than a theorem because no one has succeeded in proving it. (Or at least hasn't published!)

1. Give a brief sketch of Goldbach's life and career. [3]

2. Write 65,794 as a sum of two primes. [1]

3. What results related to Goldbach's Conjecture have been proved? How close are they to the conjecture? [3]

4. Suppose that we knew Goldbach's Conjecture could not be proved. Would that mean it wasn't true? Explain! [3]

Bonus.

Goldbach's Conjecture would have been readily comprehensible to classical Greek mathematicians. Did they make any conjectures about prime numbers that are still unsolved? [1]

Department of Mathematics

Trent University