How many ordered pairs of prime numbers (a, b) are there such that a+b = 100?

First we need to collect all prime numbers from 1 to 100.

List of such prime numbers is {2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97}

Now we have to make pairs of two numbers from the above list such that sum of both numbers is 100.

To do that we can pick two numbers, one from start and other from end so that sum is 100.

Now we will get following pairs which has sum 100.

{(3, 97), (11, 89), (17, 83), (29, 71), (41, 59), (47, 53)}

Which are total 6 pairs.

Hence final answer is 6.

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