Goldbach Conjecture

Every even integer greater than 2 can be expressed as the sum of two primes — unproven since 1742

Hover over a bar to see prime decompositions
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∀ n ∈ 2ℕ, n > 2 : ∃ p, q ∈ ℙ s.t. n = p + q

The Goldbach comet shows r(n) = the number of ways to write n as p+q for each even n. The Hardy-Littlewood conjecture predicts r(n) ~ 2C₂·n/(ln n)² where C₂ = Π (p-1)/(p-2) ≈ 0.6601 over odd primes p. Verified up to 4×10¹⁸.