|Totally agree with you on the O (Log n) without more detail, I said that from outset.
I still am intrigued by your first part so let me throw you two very famous algorithms.
Quadratic sieve - Wikipedia[^]
General number field sieve - Wikipedia[^]
Both run forever and we rate them in MIPS-years because we expect them to never end.
In fact I know several maths departments have had them running for years with prime
numbers slowly being added to a file list as it finds them.
This one has been going 9 years, and hasn't output a number in over a year and it may
never put out another number ( Only the PRIME GODS know).
Great Internet Mersenne Prime Search - PrimeNet[^]
You will note the weird today stats on right hand side to even know it is still running
and you may get a laugh from the youtube video about the notification failing and the
discovery date being 3 months late.
Wikipedia and everyone I know calls them an algorithm .. except they fail your definition
they be finite and terminate
A prime number search meets the EXACT OP QUESTION, it is an infinite search and sieving is O(Log n)
Prime Factorization using Sieve O(log n) for multiple queries - GeeksforGeeks[^]
Sieve theory - Wikipedia[^]
My problem is you can't guarantee you can do it without knowing the data behaviour and if I can sieve it.
You claim such a thing can't be done and we shouldn't talk about it ... yet it exists .
I keep answering because you keep making out some sort of authoritative answer, you insist on
some definition but you never say by who, what authority?. I have shown you a number of
computer programming fields who don't agree with that definition and things you say are
impossible exist, so I am never going to agree with you. You are wasting time trying to argue
authority in such a situation. I don't doubt your definition may be true in your field and you
really truely believe it, but that doesn't work universally.
In vino veritas
modified 30-Oct-17 1:10am.