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MBM:
I guess this begs the difference of the meaning or import of these distinctions. Again, as you note, if there are an infinite number of these prime and composite numbers - I could see how someone would argue that this difference isn't even as significant as the difference between different grains of sand on the Earth?
Let me be sure I'm understanding your point... Are you saying that just because a particular category may have a very large number of members - or even infinitely many members - that there is therefore no difference between individual members of the category?
.... Wouldn't you say there was a difference between yourself and your child regardless of the population of the planet?... No matter that there are 4 million people on earth or 4 billion or even 4 trillion, aren't you different from your child?
Yes.. there are infinitely many primes but we can still make meaningful distinctions between them.
The phrase "an even prime number" points to a unique number: the number 2. There is only one number that answers to this description. The phrase "an odd prime which divides every number which ends in 0" names the number 5 and no other number. We can give a ton of further examples ...
By the way, could you so easily distinguish yourself from every other human being on the planet? You know, for example, that you're not the only Michael Moore... You might say that no one else has your DNA... But could you articulate exactly what makes your DNA different from everybody else's? ...
And yes there are infinitely many primes that leave a remainder of 1 when divided by 4
AND ALSO infinitely many primes which leave a remainder of 3 when divided by 4...
BUT these two classifications make a
clear distinction between the numbers 41 and 43 - which also happen to be twin primes by the way - but that's another subject ...
The phrase "the black guy" might not distinguish you from every other human being on the planet. But it might be enough to distinguish you from everyone in your place of employment. Just so, the phrase "a prime which leaves a remainder of 1 when divided by 4" is not enough to distinguish 41 from 5 or 13 or 17. But it is enough to distinguish it from 43. If we wish, we could further distinguish 41 from 5 or 13 by adding that it also leaves a remainder of 1 when you divide it by 8 ...
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Additionally, on a number line, there are an infinite number of points between any two numbers on that line. Hence - it seems that if this concept of numbers (as we understand it) is valid, then numbers and math are just as fluid and soft and relative as any other man-made concept - like love or niceness or - as you mention - justice. No?
You think like a Topologist: that branch of mathematics which studies the qualitative (as opposed to quantitative) aspects of space. From this point of view there's no difference between a doughnut and a coffee cup. If you imagine that these objects were made of rubber or some other flexible material, then you could distort one object into the other without doing too much violence (like ripping or tearing). Just think of the doughnut hole as corresponding to the hole between the cup and handle.
From this perspective, there's no difference between any two open-ended intervals on the number line. So your observations are good from this perspective.
But again, it depends on the point of view you choose to take. From one point of view, there are qualities that you have, MBM, that make you just like other people (your race or your name for example). But there are also qualities you have which make you unlike anyone else...
The number 2 is like infinitely other numbers in being even. It's unlike any other in being an even prime.
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Far from being trivial, many throughout the ages have asserted that God is, in fact, the ultimate mathematician.
God may be the ultimate mathematician - but so what? What does that mean? Since God is the ultimate message board designer or gangsta rapper or cribbage player or pencil maker - is there real meaning or significance to this point in terms of us better understanding the meaning of numbers or math?
It makes more sense if one understands mathematics not as the science of number but rather as the
science of order. Mathematicians don't study numbers. We study patterns. We study order, structure, and relationship in their purest manifestations. (A mathematical equation is in essence an assertion of relationship - numerical identity - between the entities on either side of the equal sign).
If you've seen the movie "A Beautiful Mind" this point is made in a dramatic way. John Nash is portrayed as someone with a gift for seeing
patterns in the world. This is probably the best portrayal of a mathematician I've ever seen in popular media. Most other things depict us as weird people who are obsessed with numbers... we're just fancy accountants some people think... No... It's not about numbers .... It's about patterns and relationships between them....
So God is the ultimate mathematician in the sense that God is the architect of the universe. The ultimate arbiter of ORDER and STRUCTURE.
I'm reading a book called "The Elegant Universe" by the physicist Brian Greene. In it, he makes the following statement:
"... the universe would be a vastly different place if the properties of the matter and force particles were even moderately changed. For example, the existence of stable nuclei forming the hundred or so elements of the periodic table hinges delicately on the ratio between the strengths of the strong and electromagnetic forces. The protons crammed together in atomic nuclei all repel one another electromagnetically; the strong force among their constituent quarks, thankfully, overcomes this repulsion and tethers the protons tightly together. But a
rather small change in the relative strengths of these two forces would easily disrupt the balance between them, and would cause
most atomic nuclei to disintegrate. Furthermore, were the mass of the electron
a few times greater than it is, electrons and protons would tend to combine to form neutrons, gobbling up the nuclei of hydrogen (the simplest element in the cosmos, with a nucleus containing a single proton) and, again, disrupting the production of more complex elements. Stars rely upon fusion between stable nuclei and would not form with such alterations to fundamental physics. The strength of the gravitational force also plays a formative role. The crushing density of matter in a star's central core powers its nuclear furnace and underlies the resulting blaze of starlight. If the strength of the gravitational force b]were increased[/b], the stellar clump would bind
more strongly, causing a
significant increase in the rate of nuclear reactions. But just as a brilliant flare exhausts its fuel much faster than a slow-burning candle, an increase in the nuclear reaction rate would cause stars like the sun to burn out far more quickly,
having a devastating effect on the formation of life as we know it. On the other hand, were the strength of the gravitational force significantly decreased, matter would not clump together at all, thereby preventing the formation of stars and galaxies.
We could go on, but the idea is clear: the universe is the way it is because the matter and force particles have the properties they do
[corresponding to specific numbers like mass] ...."
I'm not a physicist but I've always been fascinated by Physics and the fact that the universe itself seems to obey mathematical equations... Starting with the simple observation that objects moving in a gravitational field follow trajectories (i.e., orbits) which are conic sections (Kepler) - ellipses, parabolas, hyperbolas, and circles. They have a precise mathematical description. Einstein's Theory of Relativity, at it's core, is a handful of equations that make extremely powerful (and accurate) predictions about objects moving through space and time. So God - the Designer of the Universe - is a mathematician in this sense. Mathematics is the language of Physics. It is apparently also the language of God.
So far, I'm not aware of gangsta rap making a difference to understanding reality beyond this planet...
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P.S. My grandfather's PhD was in math so I had similar conversations with him growing up. It makes me smile to discuss this again with you HB!
Very good...
Maybe if I'm fortunate enough I'll have these conversations with my children and grandchildren one day ...
I'd love one day to be able to take my kid out with a telescope and marvel together at the night time sky ...
) at the very begining of the universe until now - He still wouldn't have even gone even one point further on the Universal Number Line. 
God may be the ultimate mathematician - but so what? What does that mean? Since God is the ultimate message board designer or gangsta rapper or cribbage player or pencil maker - is there real meaning or significance to this point in terms of us better understanding the meaning of numbers or math? 
So, if this has been asked & answered, I apologize! 
to you for your choice, though!
I also really like Bell Hooks - she is so on point and I've gained a clearer picture of contemporary issues - male and female - through her. And E Dandicat's books. And so many more yet to read...