# 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.

### Comments for Prime Number Formula - Algebra

 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 www.solving-math-problems.com

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