## Composite integer function

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• You might be interested in the following two variable function. Define F(m,k) recursively as follows. F(1,1) = 15 F(m+1,k) = F(m,k) + 4*(2*m + k + 2) F(m,k+1)
Message 1 of 2 , Nov 17 4:16 PM
You might be interested in the following two variable function.

Define F(m,k) recursively as follows.

F(1,1) = 15
F(m+1,k) = F(m,k) + 4*(2*m + k + 2)
F(m,k+1) = F(m,k) + 2*(2*m + 1)

Then for both m and k positive integers,
F(m,k) = (2 * m + 1) * (2 * m + 2 * k + 1)

which makes it evident that every odd non-square positive composite
integer appears in the table, and that no prime appears in the table.

This function could be used to make an efficient prime number sieve.

Note that F(m,0) = (2*m+1)**2

Factoring a positive integer z is equivalent to finding it in the table.
• Hello Kermit, it seems that my emails can t reach you due to some unexplainable blacklist on some router near you. So I answer on the list : ... ... can
Message 2 of 2 , Nov 18 8:32 AM
Hello Kermit,

it seems that my emails can't reach you
due to some unexplainable blacklist on some router near you.
So I answer on the list :

Kermit Rose wrote:
> You might be interested in the following two variable function.
<snip>
> Factoring a positive integer z is equivalent to finding it in the table.