The twin prime conjecture
Primes keep turning up in pairs just two apart — forever? Simple to ask, brutally hard to prove.
What makes this fascinating
Primes that come in pairs — Like 11 and 13, or 17 and 19 — pairs just two apart. Do they keep appearing forever?
A stunning 2013 breakthrough — Yitang Zhang proved infinitely many prime pairs lie within 70 million; collaboration soon shrank the gap to 246.
But two is still out of reach — Closing that final gap from 246 down to 2 remains unproven.
Frequently asked questions
- What is the twin prime conjecture?
- It conjectures there are infinitely many pairs of primes that differ by 2 — like 11 and 13, or 17 and 19.
- Has the twin prime conjecture been proven?
- Not yet. In 2013 Yitang Zhang proved there are infinitely many prime pairs separated by some bounded gap, later reduced to 246 — but closing it all the way to a gap of exactly 2 remains open.
- Why does it matter?
- It probes how the primes thin out as numbers grow yet keep clustering close together — a central question about the deep structure of the integers.
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