Born to do Math 36 – Metaprimes (Part 2)
Author(s): Scott Douglas Jacobsen and Rick Rosner
Publication (Outlet/Website): Born To Do Math
Publication Date (yyyy/mm/dd): 2017/04/12
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Rick Rosner: A is 2 and B is 3. And then in the most compact representation, now, you can go either A^2 or C. In our setup, in the natural numbers, it goes A, B, A^2, 2, 3, 2*2. And then you can, again, ask whether the next number is C or AB. So at every point, you’ve got a choice to make between throwing in another prime or throwing in a composite. There’s always a new set of composites based on the next—
The numbers begin to become defined because of the relationships you’ve already specified.
Scott Douglas Jacobsen: So I see two things there. The linguistic representation would probably be conditionals. If this, then this, and if this, then this, and if this and this, then this and this, and this continues indefinitely for primes, twin primes, sexy primes, and so on.
RR: The most compact set of relationships is the natural numbers because there is a value at every possible node on the number line. Every point on the number line that is created by adding 1 to the previous number.
SDJ: Why not integers as well? Why not add integers on the number line?
RR: I dunno. The next simplest or next most compact representation is probably—is, I dunno if it the next most compact, but another easily seen representation that is pretty compact is the primes minus 2. The set of primes without 2 as a prim, and then your pattern goes A3, B5, C7, A^2 – which is 9, D – which is 11, E – which is 13, AB – which is 15, and that’s generates the set of odd numbers. If you carry it out so that whole deal is as compact as it can be.
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