14 (not a prime)
When I got back, Matt showed me his plan of attack. It was strange, and my first thought was that he was pulling my leg. But he'd done crazier things in the past without an explanation, so I rolled with it.
He pinned some A4 sheets up on the wall with a big spiral he'd drawn across them. It started in the middle, labeled "10150." He'd written "10160" at the very end of the spiral, which was so high that he had to get up on a chair to reach it.
"Okay, this represents all digits between ten to the power of 150 and ten to the power of 160. I've split it into ten segments: ten to the power of 151, ten to the power of 152 and so on... See the red points?" The spiral was peppered with red dots, which seemed to have been placed randomly. "These are trivial prime numbers. Or rather, numbers that are probably primes but can't generate profit for us because they're easy to find."
He marked some more red dots then got off the chair. "With our current computing capacity, we need up to ten hours to determine whether a random number is a prime or not. The question is, where should we dig to find the number?"
Like a fool I asked him if there was a method to find a gold vein of primes. He burst out laughing: "Well, if such a technique existed we'd never make a living from this... The big boys would leave us in the dust. They're almost certain that all these numbers are located at random; even if you're an expert in primes, you don't stand any better chance. Random means that they can be found in lumps scattered anywhere on the spiral."
So I figured it was better to tap into lumps. He nodded. "Yes, but there are many factors we need to consider. We know, more or less, the quantity of prime numbers in each segment – it's given by a function called Big Pi."
When I looked at the value of Big Pi in the section of ten to the power of 152, I saw Matt had written a giant figure. I pointed at it.
"Yeah, there are many primes in this segment," he replied, "but there are also many other numbers. Relatively speaking it has hardly any prime numbers – about one in a thousand.
"And remember, the shorter the number the less time it takes to find it. On average, we need ten times longer with the same computing capacity to evaluate a number of 160 digits compared with a number of 150 digits. So why shouldn't we take the shortest ones? Because we have rivals, and they could also tap into the short numbers. Imagine delivering a number only to hear it's already been found by someone else! It's about the gold veins; right beside the trivial numbers... there could be nontrivial ones. It's potentially a big gain for little cost, but of course everyone else is looking there too."
I was thinking about everything he'd said, when I noticed an untouched segment of the spiral in ten to the power of 153. I told him we'd dig right here. To my surprise he agreed, and returned to his computer. Of course I chose randomly; but I had a feeling. And sometimes it pays to trust your gut.
Three weeks passed in tedious waiting. I said goodbye to my villa in Miami. Our machines worked hard but they just couldn't find any new prime numbers. Sometimes they worked on a single number all day long because it had so many digits.
In the meantime, the ministry had confirmed our first prime, so I sent their payment plan to the bank. But I had to wait for one of their damned trainees to read it and open a credit line so we could invest more money in new machines.
One morning while I was reading, Matt received the long-awaited notification – we'd found another prime! I'd never felt so relieved in my whole life – when something like this works once, it could be a fluke, so you can't really build your dreams on it (much as I'd wanted to). But when you have a second success, I think it's fair to say you've found the goose that lays golden eggs!
We high-fived and he downloaded the number to the USB stick. I made a call to my buyer, then sped off in my Opel, whistling to myself. My villa in Miami reappeared: it was still so far away, but now it had color... white bricks and blue glass.
About halfway to my destination I got a funny feeling in my stomach, which I put down to stress... But my instincts were right: an SUV braked hard in front of me, at maybe the most isolated spot on the route.
I knew what this was, so I played the fool. Two bruisers yanked me out of the car and roughed me up. I took a hit right in my back, and couldn't breathe. I tumbled away, off the road and into an alley. Cars whooshed past, their drivers choosing not to see. They frisked me and took the memory stick. Then they pulled me upright and softened me up with a few punches; I'd no fight left now they had the key. One of them spoke, the smarter one, I guess: "You've got a new job, buddy! Now you're working for MegaPrimes! When you sons of bitches find a new number, you'll bring it to MegaPrimes and we'll pay you a good price. But if you give it to someone else, I promise you, motherfucker, if you do – if you don't bring it to us immediately and hand it over politely – we'll make a bonfire of your fucking business and throw you on the top. Understand?"
He waved the USB stick before my eyes. "And this is your gift to thank us for such a professional opportunity."
I'm no pushover, but I was so shaken that I got down on my knees and closed my eyes, swaying gently, waiting for them to drive away. When they'd gone, I cried a little to ease the pain.
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