"Who cares?" she said at last. "It's not like anyone's going to use it anymore."

Prime numbers are divisible only by 1 and by themselves. They hold their place in the infinite series of natural numbers, squashed, like all numbers, between two others, but one step further than the rest. They are suspicious, solitary numbers, which is why Mattia thought they were wonderful. Sometimes he thought that they had ended up in that sequence by mistake, that they'd been trapped, like pearls strung on a necklace. Other times he suspected that they too would have preferred to be like all the others, just ordinary numbers, but for some reason they couldn't do it. This second thought struck him mostly at night, in the chaotic interweaving of images that comes before sleep, when the mind is too weak to tell itself lies.

In his first year at university, Mattia had learned that, among prime numbers, there are some that are even more special. Mathematicians call them twin primes: pairs of prime numbers that are close to each other, almost neighbors, but between them there is always an even number that prevents them from truly touching. Numbers like 11 and 13, like 17 and 19, 41 and 43. If you have the patience to go on counting, you discover that these pairs gradually become rarer. You encounter increasingly isolated primes, lost in that silent, measured space made only of ciphers, and you develop a distressing presentiment that the pairs encountered up until that point were accidental, that solitude is the true destiny. Then, just when you're about to surrender, when you no longer have the desire to go on counting, you come across another pair of twins, clutching each other tightly. There is a common conviction among mathematicians that however far you go, there will always be another two, even if no one can say where exactly, until they are discovered.

Mattia thought that he and Alice were like that, twin primes, alone and lost, close but not close enough to really touch each other. He had never told her that. When he imagined confessing these things to her, the thin layer of sweat on his hands evaporated completely and for a good ten minutes he was no longer capable of touching anything.

He came home one winter day after having spent the afternoon at her house, where she'd done nothing the whole time but switch from one television channel to another. Mattia had paid no attention to the words or the images. Alice's right foot, resting on the living room coffee table, invaded his field of vision, penetrating it from the left like the head of a snake. Alice flexed her toes with hypnotic regularity. That repeated movement made something solid and worrying grow in his stomach and he struggled to keep his gaze fixed for as long as possible, so that nothing in the frame would change.

At home he took a pile of blank pages from his ring binder, thick enough so that the pen would run softly over them without scratching the stiff surface of the table. He leveled the edges with his hands, first above and below and then at the sides. He chose the fullest pen from the ones on the desk, removed the cap, and slipped it on the end so as not to lose it. Then he began to write in the exact center of the sheet, without needing to count the squares.

2760889966649. He put the lid back on the pen and set it down next to the paper. "Twothousandsevenhundredsixtybillioneighthundredeightyninemillionninehundredsixtysixthousandsixhundredandfortynine," he read out loud. Then he repeated it under his breath, as if to take possession of that tongue twister. He decided that this number would be his. He was sure that no one else in the world, no one else in the whole history of the world, had ever stopped to consider that number. Probably, until then, no one had ever written it down on a piece of paper, let alone spoken it out loud.

After a moment's hesitation he jumped two lines and wrote 2760889966651. This is hers, he thought. In his head the figures assumed the pale color of Alice's foot, standing out against the bluish glare of the television.

They could also be twin primes, Mattia had thought. If they are…

That thought suddenly seized him and he began to search for divisors for both numbers. 3 was easy: it was enough to take the sum of the numbers and see if it was a multiple of 3. 5 was ruled out from the beginning. Perhaps there was a rule for 7 as well, but Mattia couldn't remember it so he started doing the division longhand. Then 11, 13, and so on, in increasingly complicated calculations. He became drowsy for the first time trying 37, the pen slipping down the page. When he got to 47 he stopped. The vortex that had filled his stomach at Alice's house had dispersed, diluted into his muscles like smells in the air, and he was no longer able to notice it. In the room there were only himself and a lot of disordered pages, full of pointless divisions. The clock showed a quarter past three in the morning.

Mattia picked up the first page, the one with the two numbers written in the middle, and felt like an idiot. He tore it in half and then in half again, until the edges were firm enough to pass like a blade beneath the nail of the ring finger of his left hand.

During his four years of university, mathematics had led him into the most remote and fascinating corners of human thought. With meticulous ritualism Mattia copied out the proofs of all the theorems he encountered in his studies. Even on summer afternoons he kept the blinds lowered and worked in artificial light. He removed from his desk everything that might distract his gaze, so as to feel truly alone with the page. He wrote without stopping. If he found himself hesitating too long over a passage or made a mistake when aligning an expression after the equals sign, he shoved the paper to the floor and started all over. When he got to the end of those pages stuffed with symbols, letters, and numbers, he wrote "QED," and for a moment he felt he had put a small piece of the world in order. Then he leaned against the back of the chair and wove his hands together, without letting them rub.

He slowly lost contact with the page. The symbols, which only a moment before flowed from the movement of his wrist, now seemed distant to him, frozen in a place that denied him access. His head, immersed in the darkness of the room, began to fill with dark, disorderly thoughts and Mattia would usually choose a book, open it at random, and begin studying again.

Complex analysis, projective geometry, and tensor calculus had not managed to diminish his initial passion for numbers. Mattia liked to count, starting from 1 and proceeding through complicated progressions, which he often invented on the spur of the moment. He allowed himself to be led by numbers and he seemed to know each one of them. And so, when it came time to choose his thesis topic, he went with no doubts to the office of Professor Niccoli, professor of discrete calculus, with whom he had never even sat an exam and about whom he knew nothing other than his name.

Francesco Niccoli's office was on the fourth floor of the nineteenth-century building that housed the mathematics department. It was a small room, tidy and odorless, dominated by the color white-the walls, shelves, plastic desk, even the cumbersome computer on top of it, were white. Mattia drummed softly on the door and from inside Niccoli wasn't sure if the knocking was for him or for the office next door. He said come in, hoping he had not made a fool of himself.

Mattia opened the door and stepped into the office.

"Hello," he said.

"Hello," replied Niccoli.

Mattia's eye caught sight of a photograph hanging behind the professor, which showed him, much younger and beardless, holding a silver plate and shaking hands with an important-looking stranger. Mattia narrowed his eyes, but couldn't read what was written on the plate.