20031109, 16:06  #1 
Jun 2003
The Computer
2^{3}·7^{2} Posts 
Prime Theory
Please tell me if this is already known or wrong. If you have the equation:
p3/2 (/ indicates division) If p is prime, then the answer will be a whole number. 
20031109, 16:18  #2 
Sep 2002
1010010110_{2} Posts 
If your equation is equivalent to (p  3)/2 [ evaluate what is in the parenthesis first then do the rest], then Yes it is true for all primes >= (greater than or equal to ) 5 because taking an odd number 5+ and subtracting 3 gives an even which is always evenly divisible by 2.
It should also work with 3 (3  3) = 0 0/2 = 0. 
20031112, 18:24  #3 
Jan 2003
6_{8} Posts 
following your theory 9 is prime
p=9 (93)/2 = 6/2 = 3 3 is a whole number, therefore 9 is prime ??????? 
20031113, 01:07  #4 
Sep 2002
2·331 Posts 
I understood the question as "given a prime P" then the formula (P  3)/2 gives a whole number and it does. With the caveat of 5+ for P.
I didn't take it as given any whole number subtract three and divide by 2 if it is a whole number then P is prime. (WN  3)/2=another whole number. The formula isn't sufficient for proving primality, it is just a effect of primes (5+) that the primes (5+) are all odd so (p  3)/2 will always be a whole number. With p=3 the answer is 0 so it is also a whole number. Just looked up, whole numbers are the positive integers and zero. Didn't remember, it is the counting numbers without zero, the whole numbers have zero. All the 5+ above could be 3+ =========== If the original was p3/2 (/ indicates division) Given a whole number p, if the answer is a whole number, then p is prime. It would not be true because odd composites 3+ will also yield a whole number. examples 9,15,21 etc. =========== clowns789 Glad to see that you are exploring mathematical formulas, discerning patterns and expressing them as formulas has resulted in the wealth of directly usable mathematics available today. examples pi*r^2 for the area of a circle, 1/2*base*height for the area of a triangle, (length of a side of a cube)^3 gives the volume. priwo Thanks for showing how you viewed the question. Forced me to be more precise in my answer and explain the underlying issue, that the answer is true because odds 3+ will result in whole number because primes 3+ are odd they will result in a whole number. 
20031113, 01:22  #5  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:


20040108, 17:09  #6 
Jan 2004
Quebec, Canada
9_{16} Posts 
Why make it complex ?
p3/2 (/ indicates division) if 'p' is prime and >= 5, then it is an ODD number. Therefore (p3) is an EVEN number Therefore (p3)/2 will always return a whole number. So this theory works not to prove a number is prime, but this proves that a number is ODD !!! 
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