QUOTE(Raijinili @ Oct 29 2010, 02:13 AM)
STOP WHINING ABOUT IT IN PUBLIC.
GOTO CHAT.
ALSO ELNENDIL WHAT IS P?
EDIT: I'll quote what I wrote:
QUOTE
Defining Primes using Factorials
When considering the last proof, you noticed that there indeed existed numbers such that n! + p was prime, but it
didn't hold true for all of them. But consider the ability to define primes using these. Because of how the last proof
is worded, you can tell that it should hit every prime with certain values of n and p. This is definitely possible if we
are trying to approach some prime number.
So: If q > n >= 1 and (n!; p) = 1 then all primes can be written in at least one form of n! + p and these forms are
unique
Consider a few examples with :
2 = 1! + 1
3 = 1! + 2 2! + 1
5 = 1! + 4 2! + 3 3! - 1 4! - 19
7 = 1! + 6 2! + 5 3! + 1 4! - 17
: : : : : : : : : : : : : : : : : :
59 = 1! + 58 2! + 57 3! + 53 4! + 35
Notice that in some cases p isn't prime. This is what was shown in Section 1, that when p is odd, it can be either
prime or composite, as long as the result is the prime number and p and n! have no common factors. This is harder to
prove but is also easier to believe when looking at using factorials to find primes because of our findings in Section
2. Also notice that since q > n, when finding a very high prime number, there should exist more and more different
ways in which to write that prime number using factorials.
And regarding uniqueness:
QUOTE
Considering when q <= n, n always has a factor of q. p does as well, so the result constantly tends to q(1), so
these terms are never really unique, so we are more interested in q > n.
Also went ahead and wrote that other paper I was meaning to write on understanding expanding polynomials better by referring to basic multiplication. Easy and neat.
This post has been edited by Elnendil: Oct 29 2010, 09:38 AM