Concept
Are there infinitely many primes p with p+2 also prime? Formally conjectured by Polignac in 1846 — open for ~180 years. In 2013 Yitang Zhang proved the first finite-gap version.
Understand it in one breath
Primes thin out — yet do "tightly bound" pairs keep appearing? Astronomical twins like (10⁹⁹, 10⁹⁹+2) are still found. The answer feels like yes, but for ~180 years since Polignac's 1846 formal conjecture no one has proved it (Euclid proved only infinity of primes, never the twin-prime conjecture). In 2013 Yitang Zhang proved infinitely many primes lie within a finite gap — and that gap has since been compressed to 246.
At a glance
Year | Person | Proven gap |
|---|---|---|
BCE 300 | Euclid | Proved that there are infinitely many primes |
1849 | de Polignac | Formulated the twin prime conjecture (gap = 2) |
2013.4 | Yitang Zhang | Gap < 70,000,000 — the first finite bound |
2013.11 | Polymath8 | Gap < 4,680 |
2014 | Maynard·Tao | Gap < 246 |
Current | Still unsolved | The goal is to reach gap = 2 |
"From tens of millions to 246." One paper by Yitang Zhang in April 2013 ignited a field that had been stalled for centuries.
Key formula
Modern applications
Research on prime distribution, analytic number theory, and connections to the Riemann hypothesis.
Beyond MathVoyage
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