What will come in the place of the question mark (?) in the following number…

Concept

In a number series, examine the differences between consecutive terms. When those differences are not constant, test whether they themselves form a recognisable sequence — an arithmetic progression, squares, cubes, or the sequence of prime numbers. Here the gaps follow consecutive prime numbers.

Application

Compute the differences between the known terms:

1. 228 − 161 = 67

2. 299 − 228 = 71

3. 372 − 299 = 73

4. 451 − 372 = 79

The gaps 67, 71, 73, 79 are consecutive prime numbers. So the gap that lands on 161 (the term just before this run) must be the prime immediately below 67, which is 61.

Therefore the missing first term = 161 − 61 = 100.

Cross-check

Rebuild the whole series forward from 100 using the primes 61, 67, 71, 73, 79:

1. 100 + 61 = 161

2. 161 + 67 = 228

3. 228 + 71 = 299

4. 299 + 73 = 372

5. 372 + 79 = 451

Every term matches, confirming the missing value is 100.