jonald_fyookball, I didn't say I had searched for that in particular.  I hadn't googled it at that time.  I hadn't considered that phrasing or consider the existence of something as simple as an "ECDSA library".

DeathandTaxes, I do not doubt the accuracy of your analogy, but to the extent I can piece things together, I intend to continue.  Your references to speed are accurate.  Though when my processing power is bottlenecked by my SSD I also have RAMDisk and can run the entire operation from RAM if I need too, though my bottleneck has actually been the processing.

If anyone can make sense of:

def inverse(x, p):
"""
Calculate the modular inverse of x ( mod p )
the modular inverse is a number such that:
(inverse(x, p) * x) % p == 1
you could think of this as: 1/x
"""
inv1 = 1
inv2 = 0
while p != 1 and p!=0:
inv1, inv2 = inv2, inv1 - inv2 * (x / p)
x, p = p, x % p
 
return inv2

Which is in Python, it would solve my dilemma.  The commas don't make sense to me (IE: "How can a comma work with the equal sign").  That seems to be the part of my program which doesn't function correctly.  Yes, my code has that as well; that's the only part of my code I don't understand piece for piece (as I had to copy and paste that part).  All I'm really trying to do is to get this code to work.  This code should just spit out the public key for addresses represented by the number 4 through the number 10.