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Chapter II Primes and Pseudo primes
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“What? Pseudo what?” Dave grimaced, shaking his head.
“Dave, grab a calculator.” Her voice was strong and nervous, almost imperative. Her grim face spoke of urgency.
“All right, all right, don't worry, girl.” He always called her 'girl' when they argued, and now he seemed to know Susan was not playing games.
“Now divide the first number on the sheet—561—by three, then by eleven and then by seventeen.”
“Yes, it can be divided evenly by these three numbers. I see,” he said, after doing some figures.
“Now subtract one from 561. You're left with 560. Divide 560 by two, by ten and by sixteen, one calculation at a time.”
“Okay,” Dave said, “560 can also be divided evenly by each of those.” He looked up at Susan. “So?”
“Did you notice that two, ten, and sixteen are three, eleven, and seventeen minus one? And did you also notice that one was subtracted from 561?”
“I'm noticing now.” Susan could tell by his voice that the curious scientist inside Dave had finally woke up.
Susan spoke quickly, garbling the words. She tried not to scream. “If you have a composed number, then you decompose it into its prime factors, then subtract one from the original number, and this new number can again be divided evenly by each and every one of them,” stressed Susan, “its prime factors minus one, then you have a pseudo-prime number.” The smile on Dave's face had disappeared. He adjusted his glasses carefully with a light touch of his hands. “Girl, some times you scare me. Let's see if you can explain this to me more slowly.”
“Okay, take the second number. It's 1105, divisible by five, thirteen, and seventeen. Then subtract one, which leaves 1104. It is divisible by four, twelve, and sixteen. Now you have the second pseudo-prime.”
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