Ruth-Aaron pair consists of consecutive numbers such that the sum of their prime factors are equal.
Ruth and Aaron are baseball players. Aaron scored 715 home runs and broke the previous record of 714 home runs held by Ruth.
The name Ruth-Aaron pair was given by Carl Pomerance. It was first noticed and solved by his colleague’s student.
The prime factors of 715 and 714 are as follows,
715 = 2 X 3 X 7 X 17
714 = 5 X 11 X 13
The sum of the prime factors of both the numbers is 29 respectively.
The mathematicians Carl Pomerance and his colleagues Carol Nelson and David.E.Penny tried to find more Ruth-Aaron pairs, Some of the few examples are given below
- 5 and 6
5 = 5
6 = 2 X 3
2. 8 and 9
8 = 2 X 2 X 2
9 = 3 X 3
3. 15 and 16
15 = 3 X 5
16 = 2 X 2 X 2 X 2
4. 77 and 78
77 = 7 X 11
78 = 2 X 3 X 13
5. 714 and 715
715 = 2 X 3 X 7 X 17
714 = 5 X 11 X 13
