How do I get an AS-number?
Solution 1:
Well, first of all, technical requirements:
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You need to have 2 independent routes to the internet. It makes only sense to have an AS if you do your own routing policy. This is checked. This also means having BGP-capable equipment.
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You need to have your own IP-Address-BLock of I think about 4000 IP addresses. This means you need to be a member of your local IP registry and run IP allocation.
Then an AS number is pretty much a formality. Given that you do not fulfill any of these 2, you possibly also have no business having an AS number ;) Sorry.
Solution 2:
(Assuming you are talking about BGP AS)
It depends on where you are located, but for the US the NRO would be from ARIN and you can read about the requirements here.
You probably should mention why you want this. If it is multi-homing, you might find it a lot easier to use a multi-homed provider and then peer with them using a private AS number. A good collocation data center likely will provide this, it is a good question to ask when choosing one.
If you do the peering to the Internet yourself, you are going to need memory for large routing tables, you will also need to make sure you route doesn't flap or it will be suppressed for a while, etc (In other words, it is not trivial). If you really do go this route, O'Reilly's BGP book is pretty good.