mersenneforum.org Odds that a Random Prime is a Number?
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 2009-09-09, 17:38 #12 Mini-Geek Account Deleted     "Tim Sorbera" Aug 2006 San Antonio, TX USA 17·251 Posts Don't forget prime time! Or prime grade beef. Mmm.
2009-09-09, 19:51   #13
CRGreathouse

Aug 2006

3×1,993 Posts

Quote:
 Originally Posted by Orgasmic Troll I think the set of all primes is pretty apparent. There's prime numbers, prime ideals, optimus prime, prime time, WSJ prime rate, prime suspect, etc. Since the set of all primes contains the set of all first derivatives of functions, it is uncountable, thus the probability that a random prime is a number is 0.
I don't see how you can conclude that. Sure, the primes in Z are countable, but there are other primes that are numbers (e.g. Gaussian integers -- though those are only countable as well).

 2009-09-09, 20:47 #14 davar55     May 2004 New York City 5×7×112 Posts There was a thread with this title started by ernst two years ago.
2009-09-09, 22:47   #15
Orgasmic Troll
Cranksta Rap Ayatollah

Jul 2003

12018 Posts

Quote:
 Originally Posted by CRGreathouse I don't see how you can conclude that. Sure, the primes in Z are countable, but there are other primes that are numbers (e.g. Gaussian integers -- though those are only countable as well).
Can you give me an example of an uncountable set of prime numbers?

2009-09-10, 04:44   #16
CRGreathouse

Aug 2006

3·1,993 Posts

Quote:
 Originally Posted by Orgasmic Troll Can you give me an example of an uncountable set of prime numbers?
No. Can you prove one does not exist?

2009-09-10, 14:03   #17
Orgasmic Troll
Cranksta Rap Ayatollah

Jul 2003

641 Posts

Quote:
 Originally Posted by CRGreathouse No. Can you prove one does not exist?
You're really expecting some rigor here? Seriously?

2009-09-10, 19:17   #18
CRGreathouse

Aug 2006

3·1,993 Posts

Quote:
 Originally Posted by Orgasmic Troll You're really expecting some rigor here? Seriously?
What else could this thread possibly be for?

2009-09-10, 20:33   #19
cheesehead

"Richard B. Woods"
Aug 2002
Wisconsin USA

1E0C16 Posts

Quote:
 Originally Posted by CRGreathouse What else could this thread possibly be for?
Well ... a general principle of this "Homework Help" subforum has been that we give the questioner some help, but don't spell out the answer in full detail.

 2009-09-10, 20:38 #20 davar55     May 2004 New York City 5·7·112 Posts And since it was Dr Silverman asking for the homework help, maybe we should just leave the formality as an exercise for him. When you do finish your homework, sir, would you inform us of the results? :-)
2009-09-10, 22:00   #21
plandon

May 2009
Loughborough, UK

22×11 Posts

Quote:
 Originally Posted by R.D. Silverman Would anyone like to try answering?
"The question is at best poorly posed."
"The question itself is wrong headed".
"Part of learning mathematics is learning to ask the
right questions.

Part of learning mathematics is learning that words such as [random]
have an exact meaning.

If I answer a question as asked, but it is not what was meant,
it should be an impetus for the OP to learn (or ask) WHY his/her question was wrong. And, IMO, if it is NOT such an impetus then the
OP should not have asked in the first place.

My assumption, upon reading a mathematical question using the word
[random] is to assume that it has its correct meaning. To do otherwise
would be an insult to the original poster, because interpreting it otherwise
would imply that the OP did not know what he/she was talking about."

"When I was an undergrad (and even for one teacher in high school), a
frequent response to a question that was poorly posed would be:

Go think about what you just asked. Get back to us when you have
reformulated your question more precisely
".

"In forcing students to not only solve problems, but also to think about
the questions they asked, they were forcing students to learn about
mathematics. Most mathematics is not learned from lecture, but by first
learning the basics from lectures, then learning to apply it ON YOUR OWN."

"One should NEVER ask questions (in any field of study), if one does not
understand the definitions of words used in the questions.

We learn by DOING, and not by sitting and having answers handed to us."

"I could have chosen to simply say to the OP You do not understand
what you are asking. Go learn the meaning of the word '[random]',
then get back to us
. OR I could also have said
From the lack of clarity in your question, I judge that you lack the pre-
requisites to understand a meaningful answer. May I suggest that you study some elementary number theory and elementary mathematical statistics and get back to us?
"

Sorry Ardy, you did ask for it.

 2009-09-10, 22:48 #22 cheesehead     "Richard B. Woods" Aug 2002 Wisconsin USA 22×3×641 Posts You didn't have to pile on so thick -- should've saved some of those.

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