Do these functions have an infinite number of values but a specific number of prime values?

[QUOTE=Housemouse;140289]Do these functions have an infinite number of values but a specific number of prime values?[/QUOTE]
Go look up the definition of 'domain' and 'range' in the context of studying functions. 
At this point, I will join Dr. Silverman and suggest that you study the elementary mathematics related to the definitions and properties of the terms that you are attempting to use. With some more of that understanding, you might realize how your question is just ridiculous.
Suggested topics: Domain, range, mapping, function (Bob: Sorry, I didn't realize that you were formulating the same sort of reply) 
Wacky
Can you please give me an example of one function that has an infinate number of values, but can be proven to have exactly 10 prime values?

[QUOTE=Housemouse;140298]Can you please give me an example of one function that has an infinate number of values, but can be proven to have exactly 10 prime values?[/QUOTE]
f(x) = x, for x = 2,3,5,7,11,13,17,19,23,29 = x^2 for all other x. 
[QUOTE=Housemouse;140298]Can you please give me an example of one function that has an infinate number of values, but can be proven to have exactly 10 prime values?[/QUOTE]Perhaps: f(x)=29x^2 ?

[QUOTE=Housemouse;140298]Can you please give me an example of one function that has an infinate number of values, but can be proven to have exactly 10 prime values?[/QUOTE]I can.
[spoiler]Let f(x) be the function such that f(x) = x for 1<=x<=29 and f(x) = 4x for all all other values of x.[/spoiler] Paul 
Housemouse,
Yes, I can. However I choose to not do so because, as noted previously, it is trivial. If, instead, you will show that you have done the "homework" that I have suggested, and still cannot formulate such a function, I will be happy to continue the discussion. 
[QUOTE=retina;140300]Perhaps: y=29x^2 ?[/QUOTE]
No. 
[QUOTE=R.D. Silverman;140304]No.[/QUOTE]f(x)=29x^2 ?

[QUOTE=retina;140305]f(x)=29x^2 ?[/QUOTE]
Although not explicitly stated, I believe that the domain is N. Now, f(x) is prime for x = 0, 4 and no other. If you accept the more general definition of prime (i.e. not restricted to just N) then f(x) will be prime i.o. (although a proof is lacking). If we allow x \in R, then f(x) is indeed prime the required number of times. 
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