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Then we may conclude that you may not be interested in this.

What do you mean by this? I was interested in article and parent, that's why I responded.

You said "really it's worse than exponential". But that's based on your own personally-interesting way of measuring n, which is inconsistent with the given way.

Here is the conventional use of Big O notation where the input is a number:

https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality...

As you'll see they are using the number of digits, not the value of the number, because the number of digits is the size of the input.

You can find countless examples of this in literature. So this is not a 'personally-interesting' way as you assert.

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