Paolo Giordano - The Solitude of Prime Numbers

"Mmm, you really are hopeless."

The truth was that Alice already knew that. She couldn't wait to show him that she could tie it. Her father had taught her when she was little. In the morning he would leave a tie on her bed and then, before going out, he'd stop by her room and ask is my tie ready? Alice would run to him, with the knot already made. Her father would lower his head, his hands joined together behind his back, as if he were bowing before a queen. She would put the tie around his neck, and then would tighten it and adjust it slightly. Parfait, he would say. One morning after the accident, Alice's father found the tie still on the bed, just as he had left it. From then on he always tied it himself and that little ritual passed away, like so many other things.

Alice prepared the knot, fluttering her skeletal fingers more than necessary. Mattia followed her gestures, which struck him as complicated. He let her adjust the tie around his neck.

"Wow, you look almost respectable. Do you want to see yourself in the mirror?"

"No," said Mattia. He just wanted to leave, wearing his own clothes.

"Photograph," said Alice, clapping once.

Mattia followed her back into her room. She picked up the camera.

"It hasn't got a self-timer," she said. "We'll just have to guess."

She pulled Mattia to her, by the waist. He stiffened and she clicked. The photograph slipped out with a hiss.

Alice fell onto the bed, just like a bride after hours of celebration, and fanned herself with the picture.

Mattia stayed right where he was, feeling those clothes that weren't his, but with the pleasant sensation of disappearing into them. The light in the room suddenly changed. It turned from yellow to a uniform blue as the last sliver of light disappeared behind the building opposite.

"Can I get changed now?"

He said it on purpose, to make her understand that he had had enough of her game. Alice seemed absorbed in thought; she arched her eyebrows slightly.

"There's one last thing," she said, getting up again. "The groom carries the bride in his arms over the threshold."

"Meaning?"

"You've got to take me in your arms. And carry me over there." Alice pointed to the hall. "Then you're free."

Mattia shook his head. She came over to him and held out her arms like a child.

"Come on, my hero," she said, teasing him.

Mattia slumped his shoulders even farther, defeated. He bent awkwardly in order to pick her up. He had never carried anyone like that. He put one arm behind her knees and the other behind her back, and when he picked her up he was startled by how light she was.

He stumbled toward the hall. He felt Alice's breath penetrate the fine weave of his shirt, definitely too close, and heard the train rustling on the floor. When they crossed the threshold, the sound of a prolonged, dry rip made him stop short.

"Damn," he said.

He hastily set Alice down. The skirt had gotten caught on the door frame. The rip was about six inches long and looked like a sneering mouth. They both stopped and stared at it, slightly dazed.

Mattia waited for Alice to say something, to give up and lose her temper with him. He felt as if he ought to apologize, but she was the one who had been so insistent on this foolishness. She'd been asking for trouble.

Alice stared expressionlessly at the rip.

"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.