The prime sum of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 32 ?
Choose one:
A) 440
B) 512
C) 550
D) 620
E) 750
Large numbers are made in two ways:   Either by taking small prime numbers and raising them to higher powers or taking large prime numbers in the first place.   31*2= 
<gadget id="calculator">31*2</gadget>
<output>62</output>
62 (large prime number)   2^6= 64 (many small prime numbers)   To get a sum as large as 32 or more, you would need some large prime numbers. So options such as 512, 700 and 750 which have small prime numbers as factors should be ignored first. 440 also splits into 11, 4( which is 2*2), 2, 5 - relatively small prime numbers.   You are left with 620 which is 31*2*2*5 (sum greater than 32)   Answer 620
<result>D</result>
The prime sum of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 32 ?