The Lock With No Key

The coding club had gone home, and Maya was supposed to be stacking chairs. Instead she was staring at the whiteboard, where Mr. Okafor had left one line before he ran off to catch his bus.

UNLOCK THE BOX. FACTOR ME: 3,431. WINNER GETS THE GOOD MARKER.

"Easy," said Maya. She grabbed a marker. It was the good one, the fat black one that never squeaked.

"It's never easy when he writes it in capitals," said Soren. He had his notebook open already.

Maya was scribbling. "Not even. Not by three, digits add to eleven. Not by five."

"Try seven," said Soren.

"Doesn't go. Try eleven yourself."

They worked in parallel, two pens, no talking, the room ticking with the sound of the old radiator. After a while Soren said, "Fifty-three."

"What about it?"

"Fifty-three times sixty-five. No. Fifty-three times sixty-four point seven something." He crossed it out. "Never mind."

Maya sat back. "Okay. It has to be two primes. He always does two primes. So somewhere between one and fifty-nine, because fifty-nine squared is more than three thousand four hundred."

"Fifty-nine squared is three thousand four hundred eighty-one," said Soren, checking. "Yeah. So one of the primes is under fifty-nine."

"So we just try all the primes under fifty-nine."

They listed them. Two, three, five, seven, eleven, thirteen, seventeen, nineteen, twenty-three, and on up. Sixteen primes to try. It took them nine minutes and one argument about whether fifty-one was prime. It isn't.

"Forty-three," Soren said finally. "Forty-three times seventy-nine. Forty-three times seventy-nine is three thousand three hundred ninety-seven. No. Argh."

"Wait, do forty-nine," said Maya.

"Forty-nine isn't prime."

"Forty-seven, then."

Soren multiplied. "Forty-seven times seventy-three." His pen stopped. "That's three thousand four hundred thirty-one."

Maya wrote 47 x 73 on the board in enormous letters and drew a box around it and claimed the good marker by holding it over her head.

And that should have been the end. But under Mr. Okafor's line, in smaller writing she hadn't noticed before, was a second line.

BONUS. SAME GAME. FACTOR THIS ONE. And then a number. A number so long it wrapped around and kept going, more than a hundred digits, marching off the edge of the whiteboard and onto the wall where someone had taped extra paper.

Maya lowered the marker.

"Same game," she said slowly.

"Same game," said Soren. "Two primes. Multiply them, you get that."

"So we just do what we did."

Soren looked at the number. He looked at it the way you look down off something high. "For the little one we tried sixteen primes. Because the smaller factor had to be under fifty-nine."

"Right."

"So for this one." He was doing something in the notebook, and his pen was moving slower and slower. "The smaller factor is somewhere under a number with about fifty digits."

"How many primes is that?"

Soren stopped writing. "Maya. It's more primes than there are seconds since the dinosaurs. It's more than that. It's more than if every computer on Earth had been trying since the Earth was made."

Maya took this in. "That can't be right. It's the same game. You said it yourself. Somebody multiplied two numbers to make it. Multiplying is easy. We did the multiplying part for the little one in like four seconds."

"We could multiply the two big primes together too. In four seconds. That's the whole thing." Soren looked up at her, and there was something almost frightened and almost delighted in his face. "Multiplying them is easy. Going backward is not."

"But it's the same operation. Just backward."

"So is stirring milk into coffee," said Soren. "Try un-stirring it."

Maya walked up to the wall and put her finger on the number and dragged it along, digit by digit, all the way to where it ran off the paper. "Somebody knows," she said. "Somebody typed this in. They picked two primes and they know exactly what they are."

"Yeah."

"And they could tell us in one second. Forty-seven and seventy-three, done. Two numbers."

"Yeah."

"And we could check it in four seconds by multiplying. We'd know instantly they were right."

"Yeah."

"But we can never find them ourselves." She turned around. "Soren. That's the strangest thing I've ever heard. The answer is right there. It's just two numbers. And the whole planet's computers couldn't find them before the sun burns out."

Soren was writing fast now, the pen scratching. "That's why nobody's stolen your mom's bank password," he said. "That's what it's for. This exact thing. Every time you buy something online, somewhere a number like that is standing in the doorway. Anybody can walk up. Only the person with the two primes can walk through."

"Because multiplying is easy and un-multiplying is impossible."

"Not impossible. Just so hard it might as well be. Those are different." He underlined something. "Nobody's proven it's actually impossible. Somebody could find a fast way tomorrow. A kid could find it. Then every lock on Earth pops open at once."

Maya came back and stood next to him and read the number again, all hundred-something digits of it, this ordinary thing made of two ordinary numbers that were hiding inside it in plain sight.

"So the whole internet," she said, "is standing on top of a thing nobody's proven is even true."

"It's standing on top of the fact that nobody's been clever enough yet."

They were both quiet. The radiator ticked.

"Mr. Okafor knows the two primes," Maya said.

"Obviously. He typed them in."

"He's going to walk in tomorrow and want us to have solved it."

"He wants us to figure out that we can't," said Soren. "That's the bonus. That's the actual bonus."

Maya looked at the good marker in her hand. Then she uncapped it and, under the enormous number, she wrote one word.

WHO.

Then, after it: who is fast enough. And she left the question mark off, because a question mark looked too finished.

She capped the marker and set it down on the tray, exactly where Mr. Okafor would reach for it first thing in the morning.