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Prime

Name: Anonymous 2007-08-20 17:57 ID:BUq/3QWA

Is there a function f such that y=f(x) will produce a prime number y for any real x?

Name: Anonymous 2007-08-20 18:14 ID:UV3+CZkb

no

Name: Anonymous 2007-08-20 18:29 ID:AoS1aTJe

Seriously doubtful

Name: Anonymous 2007-08-20 18:31 ID:UV3+CZkb

Not unless you define the function to only graph primes.

Name: Anonymous 2007-08-20 18:39 ID:BUq/3QWA

Is there any proof there is none?

Name: Anonymous 2007-08-20 19:02 ID:P+Rv764C

If there is, email me and we'll split the million

Name: Anonymous 2007-08-20 20:06 ID:lR5lZtU7

There are infinitely many such functions.

Here's an example:
f(x)=7

Name: Anonymous 2007-08-20 20:11 ID:73UWb9OI

>>1

y = 2

(Or did you mean to say "unique prime number?")

Name: Anonymous 2007-08-20 20:12 ID:73UWb9OI

>>7
>>8

Wha-wha-what?
HIVEMIND?

Name: Anonymous 2007-08-20 21:00 ID:NNJPoSVD

>>1
who knows, there might be, you will go down in history if you find one.

Name: Anonymous 2007-08-20 22:12 ID:lR5lZtU7

>>8
If he meant unique then the answer is no, because the cardinality of the reals is greater than that of the primes. If he also meant integers instead of reals, then the answer is yes, and there are infinitely many such functions. Finally, the question becomes interesting if you constrain the function in certain ways.
See also: http://en.wikipedia.org/wiki/Formula_for_primes

Name: RedCream 2007-08-20 23:22 ID:i8o33pJP

Boy, these frickin' primes are annoying.  Why can't we generate them?  Isn't "divisible only by itself and 1" a well understood property?  Is it possible that there's a N-dimensional form of the Ulam Spiral that lines them up precisely?

Name: Anonymous 2007-08-20 23:38 ID:eqzHSSan

Let p_n be the n'th prime, where p_0 = 2. Define f:N->N by f(n) = p_n.

Name: Anonymous 2007-08-21 1:01 ID:bajxLbyD

>>12

And here I thought you were above mere academic book-learnin'. Straying from your values, are you?

Name: Anonymous 2007-08-21 3:16 ID:YD+a3oAh

>>14

>>above
Below*
He's been working on that one for the past few weeks. Let's congratulate him on a job well done!

Name: Anonymous 2007-08-21 5:15 ID:tV+1ILpM

>>12

No, wait, thread over, he's cracked it.

Fucking idiot

Name: Anonymous 2007-08-21 9:01 ID:NxGHKuJs

Name: RedCream 2007-08-21 12:51 ID:LlSq1tsH

>>14
When book learning and structured education are mis-applied to reality, then they deserve contempt.  Since you're obviously about as mentally flexible as a cicada, I'm sure you have no idea what I just said.

Name: Anonymous 2007-08-21 18:29 ID:YD+a3oAh

>>18
I could have shit that same sentence when I was 2 years old.

Name: Anonymous 2007-08-22 0:34 ID:yO9yFTGh

Optimus?

Name: Anonymous 2007-08-22 0:56 ID:Heaven

>>18

i'm pretty sure redcream is a highschool drop out who gots him some street smarts from his coworkers at mcdonalds.

Name: Anonymous 2007-08-22 2:20 ID:XgPud844

>>1
Your question is often phrased "...such that p(n) will produce the n-th prime number for any integer n" to avoid ownage by >>7 and >>8.

And the answer is yes. Here it is:

p(n) = {
2 _ n=1
3 _ n=2
5 _ n=3
.
.
.

Perhaps you should be asking whether such a function can be defined algebraically.

Name: Anonymous 2007-08-26 23:17 ID:QqZYa3Zd

>>22
>to avoid ownage by >>7 and >>8.
God damnit, I loled.

Name: Anonymous 2007-08-27 6:18 ID:+LHKu4/J

On a related note, I sure could use a way to easily find the prime factors of an integer N given the prime factors of N-1.

Name: Anonymous 2007-08-27 12:13 ID:bBmksZgo

>>24

this is relevant to my interests

Name: Anonymous 2007-08-28 13:46 ID:gZQA/rF6

Try f(x)= (x-x) + 3

For any input (x), the result will be a prime number.

Name: Anonymous 2007-08-28 17:41 ID:oL+5To/k

>>26

LOL

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