Question 66

Which of these square numbers cannot be expressed as the sum of two prime numbers?

Solution

odd + odd = even

odd + even = odd

2 is the only prime number, so if the sum of distinct prime numbers is odd, one of them must be 2 and sum of 2 and an odd number is odd

odd

a. 81 = 79 + 2

79 is a prime number , 81 is the not the answer

b. 121 = 119 + 2 

   119 is a prime number , 121 is not the answer

c.144 = 142 + 2 , 142 is not a prime number so 144 is the answer

d.49 = 47 + 2 

47 is a prime number , 49 cannot be the answer


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