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Prime Number Formula - Algebra

by Sha
(Atlanta, GA)










































prove or disprove the following: the expression n2-n+41 produces a prime number for every positive integer n. hint the following numbers 1, 10, 41.

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Mar 15, 2012
Prime Number Formula
by: Staff


Question:

by Sha
(Atlanta, GA)

prove or disprove the following: the expression n² - n + 41 produces a prime number for every positive integer n. hint the following numbers 1, 10, 41.



Answer:

This formula does not always yield prime numbers:
Formula that yields prime numbers.

n² - n + 41

if n = 1

n² - n + 41

= 1² - 1 + 41

= 41

41 is a prime number
(41 is the sum of three consecutive primes, 41 = 11 + 13 + 17)


if n = 10

n² - n + 41

= 10² - 10 + 41

= 131

131 is a prime number
(131 is the sum of three consecutive primes, 131 = 41 + 43 + 47)


if n = 41

n² - n + 41

= 1681 - 41 + 41

= 1681

1681 is a COMPOSITE number.
(1681 = 41*41)



Thanks for writing.

Staff
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