Three of the following four number-pairs are alike in a certain way and thus form a group. Which number-pair does NOT belong to that group? (NOTE: The relation should be found without breaking down the numbers into its constituent digits)

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Let's analyze the pairs:

1. 83, 97: Both are prime numbers. The difference is 14.
2. 73, 79: Both are prime numbers. The difference is 6.
3. 61, 71: Both are prime numbers. The difference is 10.
4. 31, 41: Both are prime numbers. The difference is 10.

Now, let's look for a pattern. All pairs consist of two prime numbers. Let's check if the difference between the numbers is the same for most pairs:
- 83 and 97: 97 - 83 = 14
- 61 and 71: 71 - 61 = 10
- 31 and 41: 41 - 31 = 10
- 73 and 79: 79 - 73 = 6

We see that three pairs (83, 97), (61, 71), and (31, 41) have a difference that is a multiple of 2 and 10 or 14, while (73, 79) has a difference of 6, which is not matching the others. However, a more precise pattern is that in three pairs, both numbers are twin primes with a difference of 10 or 14, but 73 and 79 are not twin primes (twin primes have a difference of 2), and their difference is 6, which is unique among the options.

Alternatively, if we look for a more subtle pattern: In three pairs, both numbers are prime and end with the same digit (61, 71; 31, 41; 83, 97), but in (73, 79), they end with different digits.

But as per the note, we should not break down into digits. So, the most consistent pattern is that in three pairs, the difference is 10 or 14, but in (73, 79), the difference is 6, which is unique.

Therefore, the pair (73, 79) does NOT belong to the group.

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