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 Housemouse 2008-08-29 12:53

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

 R.D. Silverman 2008-08-29 13:10

[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.

 Wacky 2008-08-29 13:13

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)

 Housemouse 2008-08-29 13:27

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?

 R.D. Silverman 2008-08-29 13:37

[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.

 retina 2008-08-29 13:38

[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)=29-x^2 ?

 xilman 2008-08-29 13:39

[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

 Wacky 2008-08-29 13:43

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.

 R.D. Silverman 2008-08-29 13:52

[QUOTE=retina;140300]Perhaps: y=29-x^2 ?[/QUOTE]

No.

 retina 2008-08-29 14:17

[QUOTE=R.D. Silverman;140304]No.[/QUOTE]f(x)=29-x^2 ?

 R.D. Silverman 2008-08-29 14:24

[QUOTE=retina;140305]f(x)=29-x^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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