What will be the next set of numbers in the series?
(2,3),(3,5),(5,7),(7,11),(11,13), _______

Options

A. `(13,15)`
B. `(15,17)`
C. `(13,17)`
D. `(13,19)`

Answer

To find the next set of numbers in the series (2,3), (3,5), (5,7), (7,11), (11,13), we can analyze the pattern in the pairs of numbers.

### Step 1: Identify the first numbers in each pair
The first numbers in the pairs are:
- 2
- 3
- 5
- 7
- 11

### Step 2: Identify the second numbers in each pair
The second numbers in the pairs are:
- 3
- 5
- 7
- 11
- 13

### Step 3: Observe the pattern in the first numbers
The first numbers (2, 3, 5, 7, 11) are all prime numbers. The next prime number after 11 is 13.

### Step 4: Observe the pattern in the second numbers
The second numbers (3, 5, 7, 11, 13) are also prime numbers. The next prime number after 13 is 17.

### Step 5: Form the next pair
Thus, the next set of numbers in the series will be (13, 17).

### Final Answer
The next set of numbers in the series is (13, 17).

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