The Number on the Locker

The math club had left a banner taped above the lockers. It said one number, enormous, in marker that had bled at the edges. Below it: First to factor this wins. The prize was a chocolate bar that had been sitting there since Tuesday.

Maya stopped in front of it with her swim bag still on her shoulder.

"It's two primes," she said. "Multiplied. That's the trick. They didn't pick a hard number. They picked two easy ones and smashed them together."

Soren read the number twice. It had twenty-six digits. "How do you know it's only two?"

"Because that's the mean thing to do," Maya said. "You multiply, you walk away, and nobody can walk it back."

Soren pulled out his notebook and wrote the number down, copying carefully so he wouldn't transpose a digit. "Okay. If it's two primes, we just find them. There's only one answer. Primes can't be broken down. So there's exactly one pair that makes this."

"One pair," Maya said. "Hiding."

They sat on the bench between the lockers. The room smelled like chlorine and old shoes. Practice started in twenty minutes.

Soren tried the small primes first, the way you'd check if a number is even before doing anything fancy. Does three go in? He summed the digits. No. Does seven? He set up the long division and his pencil scratched for a while and the answer came out ragged, a remainder, no good. Eleven, no. Thirteen, no.

"This is going to take forever," he said, and he was not complaining, just measuring.

"That's the point," Maya said slowly. She had her chin on her knees. "Multiplying took them ten seconds. Going backward is taking us the whole afternoon and we're not close."

Soren stopped his pencil. He looked at the two directions like they were two different staircases, one short and one that went down past the basement.

"It's lopsided," he said. "The math isn't fair in both directions."

"Right." Maya sat up. "Forward is a slide. Backward is a wall."

A seventh grader named Priya was spinning her combination lock two lockers down. Click, click, click. The lock popped open.

Maya watched it for a second too long, the way she did when something fit a shape in her head she hadn't named yet.

"Priya," she said. "How many numbers in your combo?"

"Three."

"And if you forgot them?"

Priya laughed. "I'd be trying every one until I died. Forty times forty times forty."

"But putting them in," Maya said. "That takes you two seconds."

"Yeah?" Priya grabbed her towel and left.

Maya turned to Soren and her eyes had gone bright. "That's it. That's the whole thing. A lock you can shut with one finger and can't open without trying everything."

Soren wrote lock, shut easy, open hard and then he stopped, because something larger had walked into the room and was standing behind the sentence.

"Wait," he said. "Maya. The internet does this."

"Does what."

"When you buy something. When you log in." He was talking faster now, building it as he said it. "They told us it's secure. Encrypted. But I never knew what was actually locking it. It's this. It's two big primes multiplied together. Anybody can see the big number. Everybody does. It's not even hidden."

Maya stared at the banner. "The big number is public."

"It has to be. That's how the lock snaps shut. Anybody can multiply, so anybody can lock a message to you. But only the person who knows the two primes can open it." He underlined infeasible without writing the rest of the sentence. "The whole thing is sitting out in the open and it's safe because nobody can do the backward part fast enough."

Maya stood up. "How big are the real ones? The bank ones?"

Soren did the thing he did, where he guessed and committed. "Hundreds of digits. Not twenty-six. Hundreds."

The number on the banner suddenly looked tiny.

"So if this one is taking us all afternoon," Maya said, very quietly, "and theirs is hundreds of digits long, then the backward staircase for a bank number is—"

"Longer than the universe has had time for," Soren said. "With every computer there is. All of them. Running the whole time."

They were both quiet. The drip of a shower head somewhere counted out seconds.

"That's why nobody's stolen everything," Maya said. "It's not a password. It's not a guard. It's just a number that's annoying to take apart."

"Math is the only thing holding it shut," Soren said. He looked almost frightened, in the good way, the way you look at a bridge when you finally see the cables. "Not a wall. Not a code somebody invented. Just the fact that multiplying is easy and unmultiplying isn't."

Maya grabbed his notebook and looked at the twenty-six digit number again. She tapped it.

"We can still beat this one," she said. "It's small. They were lazy. They probably used primes close together, because that's what people do when they make it themselves."

Soren caught it. "Close together means close to the square root."

"So we start at the square root and walk outward."

They did it together, sharing the pencil. Soren found the square root roughly, a thirteen-digit number, and Maya started testing odd numbers just above and below it while he checked her arithmetic. Three tries. Five tries. On the eighth try the long division came out clean, no remainder, the wall turned into a door, and there it was, one prime sitting next to its partner like two halves of something that had been waiting to be found.

"Got it," Soren breathed. He multiplied them back to be sure. The banner number came out exactly.

Maya didn't reach for the chocolate. She was looking at the two primes on the page.

"Somebody chose these," she said. "On purpose. To hide them."

"And we found them because they made it small." Soren wrote two primes, found and then drew a line under it. "The real ones nobody finds."

The bell for practice rang. Down the row of lockers, every combination lock hung shut, click click click, all those tiny walls that opened in two seconds for the people who knew, and stayed shut against everyone else.

Maya peeled the banner off the wall and folded the giant number into her pocket.