How to get MIN and MAX of Consecutive Numbers

Thank you for helping me,

It was a bad example for my problem,

What if,
10 4111
10 4112
10 4113
10 4120
10 4121
10 4122
11 4000
11 4001
11 4002
11 4010
11 4011
11 4012


Result desired would be
10 4111 4113
10 4120 4122
11 4000 4002
11 4010 4012

I know, and i am sorry for my first example, i just can't find a way to make it work, i've attached also a list with raw data.

Here it is another example. I have two columns A1 is ID, and B1 is ID_NB
ID ID_NB
10 4115
10 4116
10 4117
10 4118
10 4125
10 4126
10 4127
11 4110
11 4111
11 4112
11 4113
11 4125
11 4126
11 4127
15 4150
15 4151
15 4152
15 4153

What I need is to group numbers from ID_NB only if them are consecutive, based on ID, extracting all the consecutive intervals only and the afferent ID.
For the above list, desired result would be:
ID Small Big
10 4115 4118
10 4125 4127
11 4110 4113
11 4125 4127
15 4150 4153

I don't even know if it's posible to do it in excel, i hope that I explained myself better this time.
Thank you once again for you patience.

First of all thank you for trying to help me out, sktneer, I am a beginner with VBA, i saw your code, and I think it's close to the result I want to achieve, my fault again, because I didn't explain my problem very well, so I've attached one more time, my sample data with the desired result on second sheet. Do you think is any chance to achieve that?

Regards,