;Task:
Write a generator of prime numbers, in order, that will automatically adjust to accommodate the generation of any reasonably high prime.

The routine should demonstrably rely on either:
# Being based on an open-ended counter set to count without upper limit other than system or programming language limits. In this case, explain where this counter is in the code.
# Being based on a limit that is extended automatically. In this case, choose a small limit that ensures the limit will be passed when generating some of the values to be asked for below.
# If other methods of creating an extensible prime generator are used, the algorithm's means of extensibility/lack of limits should be stated.


The routine should be used to:
* Show the first twenty primes.
* Show the primes between 100 and 150.
* Show the ''number'' of primes between 7,700 and 8,000.
* Show the 10,000th prime.

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Show output on this page.

'''Note:''' You may reference code already on this site if it is written to be imported/included, then only the code necessary for import and the performance of this task need be shown. (It is also important to leave a forward link on the referenced tasks entry so that later editors know that the code is used for multiple tasks).

'''Note 2:''' If a languages in-built prime generator is extensible or is guaranteed to generate primes up to a system limit, (2<sup>31</sup> or memory overflow for example), then this may be used as long as an explanation of the limits of the prime generator is also given. (Which may include a link to/excerpt from, language documentation).

;nice site to check results:
Website with vast count of primes. Small ones for the first 10000 and up to 1,000,000,000,000 aka 1E12, divided in subranges : "Each compressed file contains 10 million primes" <br>
http://www.primos.mat.br/indexen.html
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* The task is written so it may be useful in solving the task &nbsp; [[Emirp primes]] &nbsp; as well as others (depending on its efficiency).
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