An Infinite Series of Primes

Timothy wandered into the piano room because it was dark and quiet. He liked his great-uncle’s house, with its fancy furniture and the huge old-time console radio, but he didn’t like being in with a mob of relatives. It was a relief to escape having his hair tousled and being told how fast he was growing.

The shiny black ebony of the piano attracted him–

“Hello, Timothy.”

Timothy jumped. It was his great-great-grandmother, calling to him from the settee. He hadn’t seen her for a year, and she was nothing like the spritely, active woman he recalled. Now she was frail, thin, and tired-looking. The oxygen cylinder with its plastic tube taped up to her nose appalled him. But he knew he shouldn’t speak of such things.

“Not interested in the party, bubeleh?” Her voice creaked.

“Not really,” he said. “It’s so….” He trailed off.

“I know. Come, sit with an old lady.”

She smelled of violets. The boy steeled himself for a hair-tousle, but it didn’t happen.

“Do you like math?”

She’d asked him this last year and he’d said no. But now… “It’s okay, I guess.”

“When I was little, I loved math. I was a prodigy.”

“You were?” He couldn’t imagine her being young.

“I could solve arithmetic problems in my head just like that. I was eight years old,” she said.

“I’ll be nine in February,” he said, and she laughed, then coughed. The oxygen tank went psss and she recovered.

“My mother was a nurse,” she said. “One day she brought me to see an old man she was taking care of at the sanatorium. His name was Georg Cantor. Have you heard of him?”

Timothy shook his head.

“He discovered infinity, you know.”


“Yes. Anyway, Cantor wanted to go home, to his wife, but they couldn’t afford a private nurse. This was during the great war, when no one had any money. One day, my mother told him I was good at math, and he asked to talk to me. She took me to a tiny hospital room, which had a strong violet scent they used to cover up the carbolic acid. Cantor was this sick old man. I could hardly say a word to him, I was so scared. I thought he might die right there. But then he told me about infinity, and he said he had a vision of it as a white light he could actually travel to.”

The tank went psss again, and they both looked at it with annoyance, and then smiled at each other.

“Really?” Timothy asked. “You can go to infinity?”

“That’s what Cantor said. But he couldn’t go in his body, only with his soul. Like to heaven, maybe.”

The boy frowned. “I don’t believe in heaven.”

“Good for you,” she said, surprising him. “I didn’t then either. Now, I’m not so sure. I want to tell you what happened. Okay?”


“Do you know what a prime number is?”

Timothy was excited. “We just did them in class! 2, 3, 5. And like that!”

“Right! You go to a good school, bubie. Now the thing about primes is, there’s always more of them.”

“I didn’t know that. Like, all the way to infinity?”

“Exactly. There’s always more, the higher you count.”

“That’s kind of cool.”

“Cantor thought so. Anyway, he asked me something from his sickbed.”

She was looking away from him, now, like she was remembering that day.

“He asked me to recite all the primes I could. 2, 3, 5… like you just started to do.”

“Wow,” said Timothy. “How far did you get?”

“Oh, very far. I told you I was a prodigy. I was sitting there on the edge of his hospital bed, and he was looking up, over my shoulder, like he was seeing something I couldn’t while I’m reciting the primes. 11, 13, 17, I was saying. 53, 59, 61…. After a while I had to start working them out. But I was a super-fast calculator back then, so I could keep going on. 337, 347, 349…. His eyes were closed, and I was wondering if I should stop, but when I paused he said, nein, Fraulein, mach weiter, mach weiter. So I did. I was getting very high up, too, but I wasn’t slowing down at all, 859, 863, 877…. It was like I was riding a train going faster and faster. 2,027, 2,029, 2,039…. I couldn’t stop. I could tell if a number was prime without even trying, like magic.”

“But how far did you get?”

“I… I don’t know. But I do remember this. Near the end I saw a white light around the old man. Everything was a blur after that. Then… well, I remember being home. My mother was sad that Cantor had died, and she was upset because she thought I’d come down with something. And I never did remember how far I got with the primes.”

“Oh. That’s too bad. Would you like me to tell you primes, too?”

“What? You can do that?”

“Sure,” said Timothy. “I’m not a prodigy. But I have this.” He showed her his tablet. “Thingy,” he said, “list the primes.”


“That’s what I call it. See? 2, 3, 5….”

“Oh,” said his great-grandmother. “Would you keep going?”

“You can’t do it anymore?”

“No,” she said. “Not for myself.”

He heard the sadness in her voice, and the eagerness, too. Timothy knew what she was asking. He knew he couldn’t say no.

“7, 11, 13….”

The funny thing was that Timothy really wasn’t all that good at math. But after a while, he didn’t have to look at the tablet anymore. And the numbers kept coming, faster and faster…. Later he couldn’t say how far he had gotten, either. But he did remember the white light and the way his great-great-grandmother smiled… as she traveled to infinity.

Laurence Raphael Brothers is a writer and technologist. He has published more than fifteen stories in the last three years in such magazines as Nature, PodCastle, the New Haven Review, and Galaxy’s Edge. Visit his webpage at for links to more stories that can be read or listened to online.

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