20080829, 12:53  #45 
Feb 2008
2^{5} Posts 
Do these functions have an infinite number of values but a specific number of prime values?
Last fiddled with by Housemouse on 20080829 at 12:54 
20080829, 13:10  #46 
Nov 2003
2^{2}×5×373 Posts 

20080829, 13:13  #47 
Jun 2003
The Texas Hill Country
3^{2}×11^{2} Posts 
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) Last fiddled with by Wacky on 20080829 at 13:15 Reason: Dr. Silverman beat me to the reply 
20080829, 13:27  #48 
Feb 2008
2^{5} Posts 
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?

20080829, 13:37  #49 
Nov 2003
2^{2}×5×373 Posts 

20080829, 13:38  #50 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
11×557 Posts 
Perhaps: f(x)=29x^2 ?
Last fiddled with by retina on 20080829 at 14:16 
20080829, 13:39  #51  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2^{2}·2,663 Posts 
Quote:
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. Paul Last fiddled with by xilman on 20080829 at 14:07 Reason: Add spoiler tags 

20080829, 13:43  #52 
Jun 2003
The Texas Hill Country
3^{2}×11^{2} Posts 
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. 
20080829, 13:52  #53 
Nov 2003
2^{2}·5·373 Posts 

20080829, 14:17  #54 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
17EF_{16} Posts 

20080829, 14:24  #55 
Nov 2003
2^{2}×5×373 Posts 
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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