Question 595147: Formulas that yield prime numbers, for example: x squared - x + 41
Select 5 numbers for X,- 0 , two even, two odd- substitute them in the formula see if prime numbers occur. try to find a number for X that when substituted in the formula yields a composite number.
This might as well be in Greek to me...
Can you please help?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Formulas that yield prime numbers, for example: x squared - x + 41
Select 5 numbers for X,- 0 , two even, two odd- substitute them in the formula see if prime numbers occur. try to find a number for X that when substituted in the formula yields a composite number.
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Prime numbers have no factors other than 1 and itself. eg, 7 = 1*7
Composite numbers have other factors, eg, 15 = 3*5
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Sub numbers for x and get the result
For zero --> 0^2 - 0 + 41 = 41
That's called f(0), the value of the function at zero.
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f(1) = 1^2 - 1 + 41 = 41
f(2) = 2^2 - 2 + 41 = 43
f(3) = 3^2 - 3 + 41 = 47
f(4) = 4^2 - 4 + 41 = 53
f(5) = 5^2 - 5 + 41 = 61
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That's 6 of them, and they're all prime numbers.
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f(41) = 41^2 - 41 + 41 = 1681 which is not prime, it's 41*41
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