The zero knowledge proof, Issue 19

We ask someone who doesn’t work as a mathematician to rule on unsolved conjectures


There are loads of statements where, despite years of trying, mathematicians have failed to determine whether they’re true or not. We reckon we’ve waited long enough: it’s time to let someone make the final call.

This issue, we ask someone who doesn’t work as a mathematician to finally decide the correctness of…

The twin prime conjecture

Two prime numbers are twin primes if one of them is 2 larger than the other: for example, 5 and 7 are twin primes. Pairs of twin primes appear to become rare as numbers get larger, but the twin prime conjecture says that however large you go, there will always be a pair of twin primes that are larger.

Twin primes

But this is still a conjecture, and mathematicians have been unable to prove whether it is true or false.

Is it true?

Alison Clarke, a doctor who works at hospital in Norfolk, has decided that the twin prime conjecture is…


As somebody who has a A-level in mathematics (B), and has read nearly
half of Vicky Neale’s excellent book Closing the Gap, I can authoritatively say that the twin prime conjecture is false.

Just think about it logically: there are lots of primes at beginning; you have your 3s, your 5s, your 7s, all bunched up like bananas. The number 2 manages to be the only even prime because it’s so small. But as numbers get bigger, the primes get more spread out, and numbers are more likely to have factors. It’s just common sense that the larger a number is, the more factors it has.

So the idea that you can have two massive numbers $x$ and $y$ where $y=x+2$ and $x$ and $y$ are both prime is just counterintuitive. If there are infinitely many primes that are just two apart, then it’s just as likely that there will be infinitely many primes that are just one apart—and we all know that that’s impossible.

Anyway, I’m off to read the second half of Vicky Neale’s book to find out if I’m right.

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