Mine the Primes

You want me to tell you about neural balls? You must be desperate. I wish you luck. Not that there's any chance of success with those things; the way they grow they're always unstable. But you're young and you've got plenty of time to squander on pointless scientific research.

But if you really insist on learning about them, I'll tell you what you need to know, rather than what you want to hear.

Fifty years ago when I was stuck on that starship, I did indeed make a serious attempt at growing neural balls for several Standing-years. I was able to culture raven brain cells well enough to grow a ball the size of a fist. The old man in charge of the department, Professor Fornerado, knew it was a waste of time, but we kept on trying nonetheless; we had no other hope of escape.

The day I completed my best attempt, having stayed awake for four solid days, spraying the surface with gluten so that it grew absolutely perfectly smooth, I chilled it and went to the Mathematics Department coffee room -- whatever the heck coffee was, I had no idea at the time.

I sat down all bleary-eyed feeling proud of myself. Then Fornerado came over to me and growled: "If it doesn't work this time, can we boil it into soup for lunch?" It hurt me to hear him say that. Maybe he didn't intend to sound so angry, but the years of hopeless frustration were crushing him like a pile of rocks. His bones were beginning to break.

"Have you measured its connective curvature yet?" he snapped as I drifted off to sleep in my comfortable chair.

"No, I--"

"Go and measure the connective curvature, young man. We can't be wasting any time." That was funny. We had wasted nineteen years so far.

It took me half the day to measure the value with interference pulses. It was totally wrong. Unless it matches the physical curvature exactly, it's no good for calculating primes. Neurons, I believe, cannot be made to grow that way, no matter how much we need them to for theoretical reasons.

I mashed up the ball and went to bed. That was the last time I considered it. I don't believe that neuro-computing has ever worked or will ever work for finding prime numbers. The few successes for getting a stable neurological calculating machine you have heard about are either errors or frauds. There must be a violation of some fundamental principle of entropy in the process. Give it up.

You have got to understand my predicament. I needed something to work. You're out here, healthy and happy. You've got the sky over your head, and all you are doing is looking for a way to make money by finding a new prime. Discover one and you'll be rich for the rest of your life. If you don't, you still have a good life. When I was struggling with this problem I had been living on the starship Erdos Cup for nineteen Standing-years. The journey from Kanin began when I was three years old. I had lived my entire conscious life -- six-sevenths of my physical life -- marooned in deep space. If all went well, the starship was on course to reach Bruken after another sixty thousand years, by which time all of us would have been long gone dead.

The trip from Kanin to Bruken was supposed to have taken fifteen hours, ship time, at close to light speed. That would have equated to twenty-eight years physical time. Unfortunately, we ran out of power on the way. You can't tell how much power is going to derive from a particular prime wavelength until it's almost used up. The brakes came on automatically as the energy fizzled so we didn't go shooting to the edge of the galaxy while we sorted it out. We had to find another prime and fit it to the drive. The process, in this type of ship, could take up to a year. Our problem was that all the primes which the captain had brought with him as spares turned out to have already been used. There was no power in any of them. We were stuck.

Look, I can see you shifting in your seat and getting bored when I tell you these things. I've seen your type before. It'll be your problem if you don't listen to me, since all you're interested in now is an easy way to make serious money. Pretty much everything you have heard about me is lies. They'll always tell you lies about the past to fool you into doing stupid stuff, like what you're trying to do now. That's how young people like you get used. The last thing anyone wants is for you to actually learn from history. Here I am: living history. You should pay attention to what I am saying. Maybe you'll discover a some better direction for your life.

When we started the journey from Kanin to Bruken there were two babies on board younger than me. At the time of which I am speaking, everyone else was an adult. A starship as big as the Erdos Cup has to be prepared to downgrade to the long-haul, because of the time it can take to fit a new prime number when the old one runs out. You have to dangle a representation of the proof of primality into the underlying twenty-six dimensional space, until along comes a wave or prime boson particle, whatever way you resolve the duality, and it resonates in the structure in a way that lets you extract its latent energy. There is only one wave-boson per prime per universe. That's it. You don't get another packet of energy from that number ever again.

While we were drifting, the captain aimed the Erdos Cup towards Bruken using the conventional rockets in the hope that we would eventually arrive here, at this planet, as a space hulk. At the very least it would provide time-capsule entertainment to your future generations, should they be interested in picking through the archaeological remains of our long-dead lives.

In the meantime, we chose voluntary extinction. Being one of the youngest, I was going to experience the worst consequences of this policy, because at the end of my life I was going to be an old man, virtually alone in a ship full of dead people. But, having had the experience of growing up for so long in confinement, I was also the one who could most authoritively oppose the idea of anyone having children and inflicting my fate of a lifetime of unnatural confinement upon them, and the next twenty thousand generations.

What a life I was living. My parents thought they were doing good by moving from Kanin to Bruken. They wanted to eventually go to Earth, the third planet of the human triangle. That would have had to wait. The ships traversed along the legs of the triangle once every twenty-one years, which was the bare minimum required for binding our three cultures together.

My mother was a painter. She was artistic... I think.

My father, he was a shit-hot salesman who could sell anything to anyone and make them feel good about it, even when it was trash. He got co-opted by the food committee to liven up our appetites. We shut the food vending machines down immediately to eliminate socially counter-productive efficiency and give people the opportunity to prepare meals. My father sold us the fashion of eating food out of snail-shell sculptures. The shells were made from ceramic and beautifully decorated by artists like my mother. The food was fiddly to extract, so meals took a long time to eat and became the social highlight of the day. When you've nothing better to do, it's a disaster to serve food on a plate and shovel into your mouth wham-bam. All that happens is you get fat and unhappy. It's one of the more important parts of life.

Me, I ate the paste because I had a lot of other things to do, intellectually. Like you, I studied mathematics. The ship's library had a complete archive of known mathematical theorems and proofs going right back to the Greeks. Thousands and thousands of years. If we were skilled enough we could add new material to it in our lifetimes. The people in our ship formed a department with over twenty active mathematicians working on various personal interests, from Set Theory to Topological Function Spaces, to... Game Theory. I was steered towards Number Theory and the computational proofs of primality, not surprisingly, in case I found the subject intellectually engaging as I grew up. It was amazing how well they kept the pressure off me. You are only really creative when you feel free. The had to contrive that.

The night after I destroyed my neural ball I was sitting in my cabin reading some old books off the computer screen when Fornerado knocked and came in. He slumped into the chair. His cheeks were sagging and hollow. He buried his face in his hands.

"The neurons can never work, can they?" he said.

I shook my head silently. All our doubts were being fully realized. I could wait till later for this fact to eat into my heart.

"Nothing is going to work," he moaned.

"What about Hyland?" I countered. "He's brilliant. Far better than anyone else here. You don't think he'll strike on something new?"

"Maybe. If he wasn't wasting all his time on Complex Manifold Cohomology. There's nothing remotely numeric about Manifold Cohomology. He's keeping away from Number Theory to avoid pressure and disappointment."

"Hm," I said.

"How are you doing? What are you reading there?"

I showed him the cover image. "Just some old book about sword fighting with dragons," I said.

"Why don't we talk about some mathematics? I'm trying to reread the proof of Goldbach's Conjecture. It's tricky. I'm finding it difficult to wrap my brain around it. What about helping me out?"

I didn't know what to say.

Fornerado shifted in his seat and looked me in the eye. "I'm sorry. I shouldn't be on to you of all people. It's... it's hopeless. People have been looking at prime numbers for generations. What chance do we have, here, now, of discovering something new just when we need it?"

I frowned and nodded.

Before he left, he said, "I didn't want to go to Bruken anyway. It was a big mistake. I was running away from two ex-wives, but I could have lived with them better than I have lived here." His elderly flesh hung from his face, making his eyes seem already dead.

It was not my fault.

I was born after the golden age of primes. The human race had squandered all the easy to find numbers as fast as they could grab them. They acted as if there was no future. What were they thinking? Did they believe that some alien civilization on the other side of the galaxy was going to get to them first, in the way that they hadn't over the last ten billion years? It was obvious: no other species in the universe was going for them. We were alone.

Luckily, the really low primes, like 13 and 127, still work for us today like slow batteries because they don't have the photon-volts to enable us suck them dry in an instant. Anyone with an engine can get energy from these prime boson-waves in sufficient quantities to run their O₂ plants, cars, and light bulbs for the next million years. Only the bigger primes have the power to deliver the kick that makes interstellar travel possible.

During the golden age, when ships ran low on energy, their onboard computers could easily find a new unused prime in a matter of seconds. When the easy-to-find ones were gone, the computations began to take minutes. Then hours. The effort goes up exponentially. Rich peoples built luxury yachts with huge computers so they could zoom off to Mercury for a business deal, then to Pluto for lunch with their mistress on some ridiculous orbiting edge-of-the-Solar-system restaurant that's only there because it sounds cool, then they'd commute back home to Earth to glance at their children before bed-time, all in a day's work.

Also, there were these private Space Jockeys who travelled further, to the stars, searching for new planets to claim and sell to future settlers, and get rich. They raised money for their expeditions by advance selling of options on their future discoveries decades in advance of finding anything. Their claims could be traded on the stock market, and their companies competed for investment, rather than sharing information. Dozens of expeditions wasted valuable energy visiting Alpha Centauri, when the first guy there could have published all his "commercially confidential" data, and saved everyone the trip. They gave misleadingly optimistic information about what they were finding, and business boomed and busted on the back of tiny rumours. Why wouldn't it? Such a system is tilted, and the money always goes towards those who lie the most successfully. It's impossible to contradict a report about something thirty-eight light years away in your lifetime, by which time the businessmen have cashed in, lived in style, and passed his inheritance on to his kids.

The Space Jockeys could have organized their search efficiently, had they shared their spoils and cooperated with information. They could have found hundreds of planets in the galaxy to explore and colonize, but they left us with only three because they wasted our chance when primes were too goddamn cheap.

By the time I was born, primes -- the proofs of primes -- had become so scarce that it took at least five years for a good mathematical institute, stuffed with computers and clever mathematicians, to get lucky and find just one. They'd sell their discovery to the highest bidder, usually one of the few starships still crawling between the three worlds. There was never enough money to buy them all, and we got what we paid for. We should have been carrying every spare prime known to man when we went into space, but the institutes didn't trust us. We bought what we could afford, and it just wasn't enough. Rather than leave us with an emergency supply in reserve, they preferred to let us rot.

Had just one prime been left spare from the golden age when they were a penny a dozen, my life would have been very different.

As the youngest mathematician on board, I knew people looked to me as if I was the one who was destined to see an answer that millions of mathematicians in history had not seen before.

Some hope.

By the morning, Fornerado was dead. No one came to tell me. I read the note on the door of the coffee room and ran away to my room in tears. Blackness closed in like ice. In my mind I saw that we were already a cold casket of bones in space. It was horrible. All I could do to get away from it all was escape into mathematics. I read the full two-volume proof of Goldbach's Conjecture (which states that every even number except two is the sum of two prime numbers) over the next thirteen days. I pondered all sorts of other mysteries to do with primes. That's how I got onto the problem of counting the prime pairs. These are primes that differ by two, like 17 and 19, or 101 and 103. It was not known if there are an infinite number of them, or whether they stop happening beyond a certain value. My mind burned with this puzzle.

In a flick of the eye, I saw the way through to the answer. One minute I was sitting there with rubbish in my head, and the next I was scribbling down mathematics as never before. I'd had a revelation. I stayed awake for three days just scrawling equations, conjectures, proofs, mostly about prime pairs. I slept with my pen in my hand and resumed writing and working out equations from the moment I woke up. When I stopped to eat I left pages of my results in the Mathematics coffee room with a note asking for someone to look. Then I'd return and work in a state of fever as long as I could stay awake and hold ideas in my head.

The next day Hyland began coming to my door about twice a day to bring food and water, and talked. He'd ask me about certain notations I used which he didn't understand. He was reading it, trying to get the ideas. He made a point of never staying for more than an hour at a time, so I could get back to what I was thinking about and continue with the breakthrough.

The result of this activity was that I discovered a sequence of new primes and a computational technique for cranking them out. These are called "Lansing" Primes, because that's my name, Pete Lansing. But I don't have any say over who uses them.

Before I was finished, Hyland and the others had read enough to help them calculate the new primes required to complete our journey. We hitched a ride on a boson, and were on our way.

I'll tell you, Bruken was like nothing I imagined it would be. You have no idea what it's like to step outside for the first time in your life. I screamed at the open sky. I went crazy. As soon as I could I moved as far away as possible from people, buildings, ships and found myself on a desert island out at sea. My parents looked after me there for a couple of years until I calmed down.

When I returned to society, irresistible political forces went to work on my life. Gratuitous space travel was re-establishing itself around the new series of primes I had discovered. In no time I was immersed in a Mathematics Department where I taught and researched for many years until I was old and my mother died. All the wealth and prestige that the world could bestow upon me came my way. I got more money than I could ask for, and I was worshipped for my genius. It's what you want for yourself, isn't it?

A new ambassador to Bruken came from Earth, by return, close to the speed of light, thirty-one years after we arrived on Bruken. He came to award me the highest honour bestowed by a government upon any member of humanity, short of actual political power and influence. He got a nasty surprise because I was no longer having anything to do with this charade.

In the intervening years my primes were squandered in precisely the same manner as they had been during the golden age. Adventurers set off in private space yachts on pointless journeys towards the centre of the galaxy. The whole industry of wasteful and entrepreneur-driven interplanetary travel sprung up once again like a nest of weeds. Celestial architects devised plans for moving distant planets closer to the sun so they could be colonized in system, totally ignoring the long-term consequential risk of collision when the access to free energy might no longer be available to avoid it.

All through this second golden age, lasting less than a lifetime, I kept shouting: "Don't squander the Primes. Don't squander the Primes." But nobody paid any attention.

At times I was put under pressure to travel to Earth, the cradle of humanity, the most beautiful world in the galaxy, they told me. Once there, I could teach my wisdom to the most gifted community of mathematicians in the history of the human race. They were following in my footsteps, hunting for new prime series like the one I had discovered. I was the one man-genius missing from the helm of their elite team. There was great money involved. It would be a triumph for humanity against the forces of darkness, they begged. I would be even more famous on Earth, where all policy is made, than in this backwater planet of Bruken. I would be better able to get my political messages across, loud and clear, to the right people, about conserving the Primes.

No. No. No. I said. I am not ever going into a starship again, for any reason whatever.

The day my father died, I quit mathematics altogether. I felt there was no longer any point to it. This was when my troubles began.

The few people still alive who had been marooned on the Erdos Cup with me, help when I get into trouble. They know they owe their lives to me. But the rest of the world turned against me. The bank stole my money and the government did nothing about it. They kicked out of my home and made up stories in the newspapers to make sure everybody who reads them hate me. You know these stories. I have never stolen from anybody, or raped anybody. They smear you and people like you believe it. The brief Lansing Prime age was drawing to a close and society got this idea in its head that it was my fault because I was refusing to work to find new ones.

The space jockeys returned from their adventures in the furthest realms of human exploration in fewer and fewer numbers. Many were not coming back as scheduled, due to the exhaustion of the prime supply.

I calculated that if the primes had been conserved, as I had demanded, we could have had starships like the Erdos Cup traversing the circuit of the three worlds and keeping us in contact for the next five thousand years. As it is, the connection looks like it'll be down forever in under fifty. I'll tell you that I am glad it's unlikely we will find a new prime sequences that we supposedly "need" in time. Prime pairs, and their reflections in the "Lansing" prime series, are a unique phenomenon. Why was everyone irrationally, optimistically, assuming that more could be found, when I -â I, of all people -- was telling them they probably couldn't? Are my words worth so little when you don't agree with them?

My crime was to publicly refute and refuse to cooperate with the project any more. I challenged their fantasy. You have what you have, you know what you are going to have, and if you throw it all away you don't deserve any more. What do you think justice is supposed to look like?

Justice indeed. Society and its leaders have tried to destroy me completely. They claimed I had been born with this natural genius of mathematical talent, so rare and valuable that it was the common property of humanity. If I sat around, lazy, and did not apply my ability as hard as I could all the time, then I was the most selfish piece of shit wrapped in skin that ever called himself human.

My brain should be cut out of me and thrown in a vat with electrodes and used as a semi-sentient neural ball.

They called for me to be forceably deposited on the next starship destined for Earth in the hope it stalled and I'd be forced to pull the same mathematical miracle, like I did last time, to get myself out of trouble.

But I've made it absolutely clear that I would kill myself if I was ever put in that position, which is why they haven't done it. But I am most concerned that they might get desperate enough to do something much more evil. One day they might round up hundred bright young mathematicians, like yourself, and dump you in that place on a ship going nowhere in the hope that you would come up with the goods before you expired.

This is not paranoia. They will do this to you if they think it will work. You mean nothing to them. They can send young men like you to war knowing that you will die. You must beware that you can be used.

So, by all means, experiment with your neural balls if you really want to. You won't get help from me. If you succeed you will get rich and famous, and if you are honest you will regret it. They will owe you for nothing, and give no more than what they think they can get from you in the future, and just enough to convince other fools like you that the reward exists. If you can't save the primes from their greedy hands, don't look for them. Leave them alone as a precious gift to future generations. They'll understand their value far more than we do. And they will be eternally grateful to you, even they don't know who you are.

You can draw strength from this knowledge. As I have done.