2b. Re: Composite number function(2)
Posted by: "djbroadhurst" d.broadhurst@...
Date: Thu Nov 19, 2009 9:10 pm ((PST))
--- In firstname.lastname@example.org
Kermit Rose <kermit@...> wrote:
> > The easiest way to find a large integer in the table
> > is to factor the integer.
> Post hoc, ergo propter hoc?
Of course. Like much of mathematical thinking, this is circular.
> > However, if some other algorithm for locating a given number
> > in the table is developed, that algorithm would also be a
> > factoring algorithm.
> Your nebulous "algorithm" was surpassed 2200 years ago:
I presume you refer to the standard sieve of Eratosthenes
for identifying prime positive integers.
I have yet to confirm whether or not the prime number sieve
based on the composite number table is more or less
efficient than the standard sieve of Eratosthenes.
You could use the Standard sieve of Eratosthenes as a composite number table.
My table differs from that of Eratosthenes in two ways.
In my table, only positive odd non-square integers are represented.
My table is not symmetric.
A given pair of factors occurs in my table exactly once.
Of course integers that are factored into pairs in more than one way
will appear multiple times.
The smallest integer to appear in my table in more than one way
105 = 3 * 5 * 7 = 3 * (5 * 7) = 5 * ( 3 * 7) = 7 * (3 * 5)