1. The problem statement, all variables and given/known data For all n is an element of N, n2 - n + 41 is prime N= natural numbers 2. Relevant equations None. 3. The attempt at a solution Let n=1 12 - 1 + 41 = 41 is prime. n2 - n + 41 is not prime. so this hypothesis is not correct. assume n2 - n + 41 is not prime. there exist n that let n2 - n + 41 = n2 so n2 - n + 41 is not prime. therefore, when 41-n=0 this equation holds. therefore there exists a n=41 that n2 - n + 41 is not prime. Hence n2 - n + 41 not true for all n is an element of N.