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# Choose an integer randomly from the set...

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Choose an integer randomly from the set 1,2,3,...,99,100. Square it, then subtract 1. What is the probability that the resulting value is a prime number?

Aug 30, 2020

#1
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The probability is 1/20.

Aug 30, 2020
#2
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I'm pretty sure that's incorrect. It's literally a giant guess, unless you explain how you got it.

Guest Aug 30, 2020
#4
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< The probability is 1/20 >

That would mean there are five of them.  What are those five numbers, please?

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Guest Aug 30, 2020
#3
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(it's correct)

Out of all the numbers 1-100, if you square 2 and subtract one, it gives you a prime. All the others don't work. I'm not too sure how this works, hopefully someone can explain.

Aug 30, 2020
#5
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Instead of using words to think about it, let's use variables and numbers!

What the problem is asking is: For what numbers 1 - 100 is n^2 - 1 prime?

First, we need to know what n^2 - 1 is. This is (n-1)(n+1). (Difference of squares?)

We see that for it to be a prime number, n - 1 has to be 1. The only number that this works is 2.