Prime the Indivisible

Prime learned to look for what things were made of in her family's shop, where hedgehogs had weighed coins for generations. As a small kit she watched her mother set a coin on the scale and frown. "This one's been mixed," her mother said, "cut with cheaper metal. A true coin has its own weight and no other." She let Prime hold a pure one and a false one, one in each paw, and Prime felt the difference — the true coin sat certain and whole, the false one heavier and wrong. That night, alone, Prime ran her paws over her own spines for the hundredth time and finally understood why they'd always felt strange. She had spent years wishing they were smooth and even like the other kits'. But they came in twos, threes, fives, sevens — never fours, never sixes — and now she saw it: those were the counts that couldn't be cut into equal smaller groups. They were like the true coins. Whole all the way through, answerable to nothing smaller than themselves. She fell asleep with a paw over a tuft of seven, feeling, for the first time, not odd but pure.

When she was twenty-two she walked to DiscreteQuest, where a wise old owl with spectacles perched on his beak met her at the door. He set down a scatter of thirty acorns and said, "Sort these for me, however you think is truest." Prime did not count to thirty. She gathered acorns into little heaps and tested each heap — could it split into equal smaller piles? A heap of six she broke into two threes and set aside as not-whole. A heap of five she pushed and prodded and could not divide evenly by anything but one or itself, so she stood it up straight and alone. She kept only the heaps that refused to break: two, three, five, seven. Then she took a broken heap — twelve — and cracked it down and down until only unbreakable heaps were left, and showed the owl how those exact small heaps, multiplied back together, rebuilt the twelve and nothing else. The owl watched her whole sorting without a word. Then he peered at the tufts of her spines, saw they matched the very heaps she'd stood up alone, and quietly opened the door.

In her own workshop, years on, a young squirrel named Pip watched her at this sorting and couldn't hold his questions. "How do you always know which ones won't break?" Prime picked up a handful of acorns. "I try to share them," she said. "Truly try." She counted seven into a row. "Seven — can I make equal groups? Two rows? There's one left over. Three rows? Leftovers again. Nothing shares it evenly but one row of seven, or seven rows of one." She tapped the matching tuft on her back. "So it stands alone. Whole." Then she scooped up twelve and did something slower. "Now, twelve will break — but I don't stop at 'two sixes.' I keep cracking. Six breaks into two and three. So twelve is two, two, three." She arranged them into that little cluster. "Every number bigger than one is either a won't-break — a prime — or it's built from a unique bundle of them. Twelve is always two, two, three, and no other bundle of primes will ever make twelve." Pip's eyes went wide. "So it's like a secret recipe. Every number has one, and only one." "Exactly," Prime said, delighted. She glanced at a clock on the wall. "Here's another wrinkle. Say it's ten o'clock and you wait three hours — you don't land on thirteen, you land on one. You wrap around at twelve." She smiled. "The world is full of numbers folding back on themselves like that. But underneath all of it are the primes. Crack anything far enough and you meet them."