Departure question
Find order without counting everythingPort 10 of 16“Through Twin Prime Conjecture: How can we find hidden order without counting everything?”
Trace recurring structure through exploding possibilities, divisibility, and the apparent irregularity of primes.
This voyage is an editorial path for understanding, not a claim of direct historical influence or sole invention.
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.
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.
Key formula
Modern applications
Research on prime distribution, analytic number theory, and connections to the Riemann hypothesis.
Beyond MathVoyage
Curated sources and problems. Bring one discovery back from OEIS, Project Euler, MathOverflow, or arXiv.
- Wikipedia
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- OEIS
No concept belongs to one person
Follow people who played different roles
These are not inventor credits. They are different ports: opening a problem, sharpening a language, or carrying it into another world.
Number lenses
A concept looks different when its world of numbers changes
These numbers are editorial lenses for the voyage, not required prerequisites.
Natural Numbers
Trace recurring structure through exploding possibilities, divisibility, and the apparent irregularity of primes.
Open the number voyage
Integers
Trace recurring structure through exploding possibilities, divisibility, and the apparent irregularity of primes.
Open the number voyage
Rational Numbers
Trace recurring structure through exploding possibilities, divisibility, and the apparent irregularity of primes.
Open the number voyage
Concept genealogy
What supports it, and what does it open?
Concepts arriving from before
Current port
Twin Prime Conjecture
Concepts opened from here
No direct successor port is curated yet.
Only direct editorial links are shown; this is not a complete learning order or historical influence line.