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 (or 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 one-paragraph 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]
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