20 (not a prime)

There I was again in the research center: me and the girl in front of the desk, the professor welcoming us. He was majorly impressed that we could comply with their 150-digit requirement. But he was surprised when I told him that I had no memory stick, and that I would type the number into his laptop. He spun it towards me, and I asked him for a cup of coffee. He grumbled, but got up.

I lowered the girl's head so that she could focus on the table, and placed a white sheet of paper in front of her. I said, "The number from earlier...". She started to dictate: seven, seven, four, six, etc. We entered the prime in less than five minutes.

The professor turned his gaze from my assistant's cold poker face to mine. He announced: "There are some changes. If you wish to continue our collaboration, you should know that we don't accept prime numbers shorter than those already delivered by you. In other words, we need at least a 154-digit number next time."

I told them facetiously that they had weird business practices, changing the rules every time.

He said: "Listen, the fact is that discoverers like you use some kind of 'vein' of primes to find numbers that are close together. And pirates know about it. Imagine you delivering us two really close primes and us using the product of those two numbers in our encryption key. The square root of our encryption key would give them a hint as to the location of your vein – in other words, they will practically know what our numbers are."

I suggested that the pirates don't work on computers 24/7 like the pros who are dedicated to these crazy calculations. The professor's face turned pale. He spoke methodically, hammering out every word:

"Let me tell you something. Recently I got reports of spikes in overnight power consumption in the building of a state-owned oil enterprise – you should know what I'm talking about. Regular as clockwork, from 11:00 p.m. to 5:00 a.m., fifteen hundred computers turn on, connect to the network, and start decrypting data. All this happened because a marketing assistant downloaded a PowerPoint file with cute kittens in it... a PowerPoint file with a virus, which took control of all the machines in that office! The pirates have millions of computers at their disposal – probably your mother's too – which they use to run their computations without our knowledge. 'Pirates' is putting it mildly...".

He pulled up the corners of his eyes to narrow them, which lent him an Asian look. "When every couple in a particular Asian country – a country where all computer parts are made, by the way – have their own computers running at, let's say, 3 gigahertz – a very modest rate – the pirates could use this potential to perform many billions of billions of operations per second. One hour would be enough to crack twenty-two-digit encryption. It's the power race that we lead. A race with high stakes.

"You will be paid, but we'll be more demanding each time, and the conditions are likely to change at every meeting."

I got up, a little stunned, before he added: "Oh, and since you're so concerned with money, you should know that we're granting a $20,000 bonus for a 200-digit prime!"

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