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November 24th, 2017, 09:06 AM  #1 
Newbie Joined: Apr 2014 From: Edmonton Posts: 5 Thanks: 0  A question about primes
Hi, I have a question about primes here. I was just wondering if any whole number plus one half could be used to find primes. for example, 1.5,2.5,3.5... The way I see it, you shouldn't round up or down from these numbers and I was wondering if anybody could establish for me the logic behind rounding up, say, from 1.5 to 2. 
November 24th, 2017, 09:16 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,814 Thanks: 1046 Math Focus: Elementary mathematics and beyond 
Once you have a candidate how would you test it for primality?

November 24th, 2017, 05:59 PM  #3  
Senior Member Joined: May 2016 From: USA Posts: 1,038 Thanks: 423  Quote:
If you round up 3.5 you get 4, which is NOT prime. Last edited by skipjack; November 24th, 2017 at 08:44 PM.  
November 24th, 2017, 09:33 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,057 Thanks: 1618 
That wouldn't stop one from asking whether, for some prime $p$ (such as 131), $q = \sqrt{4p163}$ is an integer, and $p + q + 1$ another prime.

December 15th, 2017, 10:52 PM  #5 
Newbie Joined: Apr 2014 From: Edmonton Posts: 5 Thanks: 0  Okay...
Seeing as how there has been no established logic about whether or not to round up or down from 1.5,2.5,3.5...etc. I think we should establish instead, logic pertaining to what makes something truly prime. If no logic stands as to why one would round up from 1.5, rather than down, we must say we can do neither. If we can do neither logically, we must never round from a .5 number above 1. I believe if we cannot logically decide how to round (up or down). Then we must therefore factor these numbers into the definition of what makes something truly prime because they will somehow alter our definition of a whole number by being somewhat of a subclass of wholes that may be used to calculate primes as well. When considering how to calculate these "new" primes we should disregard 0.5 in our calculations. Logic dictates we round down from 0.5 instead of up. The following groupings show that on the number line 0.5 should be rounded down because 0 is the absence of quantity and this should be considered when rounding from 0.5. 0.1, 0.2, 0.3, 0.4, 0.5 versus 0.6, 0.7, 0.8, 0.9, 1.0 As you can see above 0.5 does indeed group nicely on the left, closer to 0. Anything above 0.5 should be rounded to one. This means that 0.5 cannot be used in the calculation of any prime numbers. ~Pegleggedninja 
December 16th, 2017, 08:05 AM  #6 
Senior Member Joined: May 2016 From: USA Posts: 1,038 Thanks: 423 
What do you mean by "prime"? For most, primes relate to whole numbers, not rational numbers like 1.5. So as I said before, what are you talking about? Rounding is about approximation. It is true that 1.5 is just as close to 1 as it is to 2. Therefore you can logically use either 1 or 2 as an approximation: your error will be the same no matter which you do. 
December 16th, 2017, 11:22 AM  #7 
Senior Member Joined: Sep 2016 From: USA Posts: 383 Thanks: 207 Math Focus: Dynamical systems, analytic function theory, numerics  

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