Your Name Is in the Number
Your prime is not a label stuck beside your name. The name is in the digits — and with a three-letter word, you can read it back out.
Imagine someone hands you a long string of digits. Twenty of them. Thirty. Maybe more. And then they say something that sounds like a magic trick:
“That number is Maya.”
Not labeled Maya. Not assigned to Maya. Is Maya. Hand the number back with a tiny three-letter word, and her name comes out of the digits themselves. No drawer of names. No phone call to a server. The number was the whole story.
That is what a reversible prime does. And it is stranger than it sounds — because primes are famous for not coming apart. You cannot factor a big prime into smaller pieces that reveal a secret. We do not crack this one open either. We build the number so the name is already inside it.
Here is how, with Maya as our guest of honor.
We start with her name. First we agree on a single spelling — uppercase, accents tidied — so both ends of the puzzle are looking at the same letters. Then we run into a problem: a name takes space, and a small prime does not have much of it.
If every letter took the same amount of room, Maya might not fit. So we write her name the way people write things they say all the time. “OK” is two letters because people say it constantly. Letters that show up in almost every name — E, A, spaces — get a short mark. Letters that almost never show up — Q, Z — get a longer one. Same name. Less room. The table of marks is fixed and shared, so nothing extra has to travel with the number. Maya is now a short string of marks ready to become a number.
But if we stopped there, anyone who knew the marks could read her name straight out of the digits. That would be a label, not a puzzle.
So we give Maya a tiny key: three characters. Something like K7P. The same word locks the writing and unlocks it. Locked, the marks become a big number that looks like… a big number. Looking like nothing is the point. That number is what goes on the certificate, what you can put on a wall or send to a friend. Without the word, a casual looker sees digits and stops. With the word, the writing opens again. A wrong word does not open onto someone else’s name — it just fails, politely. Three letters is on purpose: a word you can read aloud, write on a card, text a friend. This is a puzzle, not a bank vault.
One more problem. Lock Maya’s marks once and you get a number. The chances that number happens to be prime are about the same as drawing a particular card from a deck. Sometimes it works. Usually it does not. And we are not in the business of handing people almost-primes.
So we add a pinch of salt.
The name is the recipe. A few spare digits spell nothing at all — they are just a pinch we get to change. Set the pinch, lock the whole thing with Maya’s word, and ask: is this number prime? Usually no. Change only the pinch. Lock again. Ask again. The letters never move. After a few tries — often dozens, almost never thousands — one of those locked numbers turns out to be prime. That is the dish we serve. That is Maya’s prime.
Reading it back is the same path in reverse, and it feels like the curtain is still half up.
You take the prime and the three-letter word. Unlock. Ignore the salt — those digits were never part of the name. Spell the short marks back into letters. Out comes MAYA.
Nobody looked her up. The number did not phone home. The digits were the name, locked and salted until they were also a prime. That is the part that still delights us: you can hold the whole puzzle in your hand as a number, and the moment you unlock it, a person walks out.
If you want the grown-up names for those three pictures: the abbreviations are Huffman coding, the lock is a 1970s reversible cipher called a Feistel network, and the pinch of salt is a nonce — spare bits we nudge until the Miller–Rabin test says prime. The full reverse walkthrough lives in How Decoding Works (Backwards Magic). Or skip the reading and try it: the decoder will take a prime and a key and hand you a name in milliseconds.
The number on your certificate is not a sticker. It can say your name back.