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Goldbach's Conjecture — Every Even Number as a Sum of Two Primes
Problem
Can every even integer be written as the sum of two primes? E.g., , has 6 representations.
Why it matters
In a 1742-06-07 letter from Goldbach to Euler. Euler's reply: "I regard it as a completely certain theorem, although I cannot prove it." 285 years later we're still in that state. The number of representations grows with — has 6 ways, has 28, near it's tens of thousands — strong heuristic, but proof is another matter.
Progress so far
Verified up to (Oliveira e Silva 2014). Vinogradov (1937): every sufficiently large odd number is a sum of three primes. Harald Helfgott (2013): every odd number is a sum of three primes — ternary Goldbach completely proved. The strong (even) Goldbach remains open.
Further reading
💡 Explore together, one line at a time(0 contributions)
Contributions are not ranked by popularity. Curator feedback names what is clear or reproducible, and peer signals mean someone understood or actually reproduced it.
What did you notice?
You do not need a complete proof. A small observation can open the next path.
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