Which of the following numbers will replace the question mark (?) in the given series?

8, 15, 26, ?, 56, 75

The correct answer is 39.

To find the missing number, we need to identify the pattern in the series:

Series: 8, 15, 26, ?, 56, 75

Let's calculate the differences between consecutive terms:

15 - 8 = 7
26 - 15 = 11
? - 26 = ?
56 - ? = ?
75 - 56 = 19

So the differences so far are: 7, 11, __, __, 19

Look carefully at the numbers 7, 11, 13, 17, 19 — these are all consecutive prime numbers!

Prime numbers in order: 2, 3, 5, 7, 11, 13, 17, 19, ...

So the differences between consecutive terms follow the sequence of prime numbers: 7, 11, 13, 17, 19

Let's verify this fills in the missing term correctly:

8 + 7 = 15 ✓
15 + 11 = 26 ✓
26 + 13 = 39 ← this is our missing number
39 + 17 = 56 ✓
56 + 19 = 75 ✓

The complete series is: 8, 15, 26, 39, 56, 75

Therefore, the number that replaces the question mark is 39.