From Goldbach's Letter to Helfgott

The Prompt

Explain the Goldbach conjecture to a reader who knows what prime numbers are. State the strong and weak conjectures; explain the difference. Cite Goldbach's 1742 letter to Euler, the computational verification by Oliveira e Silva (2013), and Helfgott's 2013 proof of the weak conjecture. Explain what Helfgott proved, what method he used (the circle method), and why the strong conjecture remains open.

Completion Criteria

A short essay (three or four paragraphs) with at least three citations — Goldbach-Euler (1742), Oliveira e Silva (2013), and Helfgott (2013) — and a clear explanation of the gap between the weak and strong conjectures.

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