Saturday, March 26, 2022

It's a Prime

Three men were sitting around a table in prison. All of them had killed. The theme of their talk was, what had they killed for.

Tom admitted "I was too besotted with a girl, I couldn't take it when she left me, so, after harrassing her a year, when she tried to defend herself, I killed her."

Dick said, "My own story is somewhat different. It's even slightly original:

"I am a fairly lawabiding man, otherwise. Just not very well educated. One day, I was sitting on a bench, and on the bench opposite, I saw a man looking a bit like a hoodlum in his trench coat.

"He was writing, writing, and then writing again, in his notebook. I was starting to get a bit curious, and thought, perhaps he was planning some crime or something.

"Suddenly he sprang up, and he shouted, full of glee 'It's a crime, it's a crime!' - there I had the proof.

"He was going to kill or extort someone, I thought I'd like to play the hero, so, I said 'I take you under a citizen's arrest' and when he refused, we started to wrestle, and I killed him.

"When the policemen came in, I explained the situation. Quietly one constable took up the notebook.

"'Are you sure,' he said, 'that he didn't shout «It's a prime, it's a prime!» instead?' - and he looked very intently at me.

"'But that doesn't mean anything, does it?' I retorted.

"But the policeman told me: 'oh yes, it does, it means, «It's a prime number.»'

"He showed me the notebook, last written page, and the crossed out numbers 673 and 677 on top, crossed out with one stroke. Below that, there were lots of funny calculations all starting with 455603 on top. Here, I'll show you one."


"Apparently, the guy had taken a multiple of 607, under 455603, and it ended in 603, and then he only needed to take care of the remainder below the first three integers, and as 438 is smaller than 607, it's not a multiple of 607."

Harry asked "wait, how is 17603 a multiple of 607?"

Dick obliged with another calculation:


"You see, by deducting 1 times from 10 times, he got nine times the prime factor. And as 5463 ends in 63, the thing he needed was a 4 added below the six, so, he took 1214, the double, and removed it one step to the left. 17603 is therefore 29*607."

Harry asked "and what was the point of all this?"

"There wasn't one," said Dick, "unless you think of it in terms of solving a pointless problem. The policeman showed me how the two numbers 673 and 677 miltiplied to 455621, and it seems 455603 was the highest prime number below that, it was definitely not either 673 or 677 away from the product of these, so they couldn't be counted either. It seems, the guy had been crossing out all prime factors, starting with 2, 3, 5, 7, 11 and 13, and after crossing out these last two had come to his conclusion after testing 661.

"I killed a man because I didn't understand his hobby."

And Harry said, "My friends, I see why you are here, I see why some others don't like you, but, frankly, you are a real treat." When they stared at him in unbelief, he added "well, at least compared to my victim!"

Tom asked "whom did you kill?"

Harry answered "I killed a shrink, he was taking away liberties from me for reasons about as stupidly thought through as Dick's here, and he was harrassing me that way about as relentlessly as you did to your ex-girl-friend. You are both better people than my victim."

Whether we believe Harry or not, I think the story has come to a conclusion. The moral for mathematicians would be, if you ever shout out you have proven a number a "prime" - please shout "it's a prime number!" so no one thinks you shout "it's a crime!"

Whether the story has a moral for shrinks, I don't know, but it has one for people who send shrinks onto someone. Please don't push people to kill.

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