Goldbach conjecture calculator

Enter any even number ≥ 4 to express it as a sum of two primes. Shows all possible pairs.

Even number

Goldbach's conjecture

Every even integer greater than 2 can be expressed as the sum of two primes. Proposed by Christian Goldbach in 1742, it remains unproven but verified up to 4 × 10¹⁸.

Examples

4 = 2+2. 10 = 3+7 = 5+5. 100 = 3+97 = 11+89 = 17+83 = 29+71 = 41+59 = 47+53 (6 ways).

Goldbach's comet

Plot the number of Goldbach representations for each even number — it creates a beautiful pattern called Goldbach's comet. Larger numbers generally have more representations.