The prime numbers between 1 to 100 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 consider two prime numbers that gives us sum 100
Lets start checking with each prime number
Sum --------------------> Ordered pairs
3 + 97 = 100 --------> (3,97)
11 + 89 = 100 -------> (11,89)
17 + 83 = 100 -------> (17,83)
29 + 71 = 100 -------> (29,71)
41 + 59 = 100 -------> (41,59)
47 + 53 = 100 -------> (47,53)
97 + 3 = 100 --------> (97,3)
89 + 11 = 100 -------> (89,11)
83 + 17 = 100 -------> (83,17)
71 + 29 = 100 -------> (71,29)
59 + 41 = 100 -------> (59,41)
53 + 47 = 100 -------> (53,47)
So, there are 12 ordered pairs of prime numbers (a,b) such that a+b=100