What is the smallest integer that is the sum of 2 distinct prime integers, each greater than 80 ?  Choose the correct choice from the following answers
A) 170	B) 172	C) 173	D) 199	E) 186
First of all, discard 173 and 199 since they are odd. Sum of two primes greater than 2 will always be even because both primes will be odd.   Both numbers need to be greater than 80 i.e. their sum needs to be greater than 160. Since two of the given sums, 170 and 172, are quite close to 160, it should be fair to assume that if they can be written as sum of two primes, we will find the primes between 80 to 90.   172etween 80 and 90, there are only 2 primes: 83 and 89 (if you don't remember this, you just need to check for 81, 83, 87 and 89)   83+89= 
<gadget id="calculator">83+89</gadget>
<output>172</output>
172 so answer is (172)
<result>B</result>
What is the smallest integer that is the sum of 2 distinct prime integers, each greater than 80 ?