SUPPOSE all composites consist of one of three types: 1) a composite * a composite (whereby +1 or -1 returns a prime or both or neither do) 2) a composite * a prime (whereby +1 or -1 returns a prime or both or neither do) 3) a prime * a prime (whereby +1 or -1 returns a prime or both or neither do)
I begin to calculate the percentage rates of prime returns, but was wondering if anyone has planed this out and found the rates to behave in what way and in what if at all variance exists between them.
2*2 is first TYPE 3 and 2*2+1 or -1 is 3 or 5 both prime so first entry is 2/2 and 100% incidence of returning a prime.
2*3 is second TYPE 3 and 5 and 7 produced 2/2 and 100% incidence of prime.
2*4 is a TYPE 2 and 7 and 9 makes it 1/2 or 50% incidence of prime.
3*4 is a TYPE 2 and 11 and 13 add 2/2 to become 3/4 or 75% incidence of prime return on tier 2 of type 2.
ETC., et al for all types plot an curve return a table, examine the differences if any exist
Interesting question to consider, when we multiple two primes, is the result number any more or less likely to be adjacent to a prime, or is just the opposite true and are multiply composites the cornerstone? Or perhaps it is the combination of the two (the TYPE 2 line) essential or interesting. In any event the world will be forever changed once the smart people (the rest of them get a handle on this). Is it possibly all three despite early differential fluctuations to plane out the same, or do they diverge or converge and where, if, when, and why, and what does this infer about physics in notions of composite structures and quantum mechanics, molecular constructs, etc. I am a little arrogant sounding but just going to let the merits of the mathematics or the ragged jealousy of the dunces prevail around me with the usual bally-who of insults I shall wear as a badge of honor, I suppose, in some system, perpetually.