Author – Andrew J Frost 12/10/2021 REV TWO PnonP p19
OBSERVATION 19 – Appendices to Part One
Appendix 1
My logical process formula for the generation of my special Set of prime and non-prime numbers: –
┌1
12n + ├5 = p(p&np) 12n + {1,5,7,11} = p(p&np)
├7
└11
p(p&np) – [div5] = S(af)
p(p&np) minus [div5]
n – is an integer
1,5,7,and 11 – are prime numbers used to raise the resultant of 12n to “p(p&np)”
p(p&np) – are [primes] and [non-primes- evolved from odd-composite numbers]
[div5] – is redundant information (i.e. all odd-composite numbers end in 5), hence the ‘minus’ which represents a sieve (or sort) to remove them.
S(af) – my Set comprises all the primes and all the non-primes composed from odd-composite numbers.
[div3] – is redundant information (i.e. all odd-composite numbers that are divisible, i.e. multiples of 3. Only Relevant to spreadsheet –20190331-nonDupl-IDprimes-DIAGS, sheet – P&nonP all-int div3+5 eq2
The prime and non-primes being completely complimentary to the extent that regular patterns are formed. The odd-composite numbers are only being formed from the product of primes; each a unique combination.
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Appendix 2
Paper by: – Sandor Kristyan (Sandor Kristyan -August 30, 2017). Hungarian Academy of Sciences, Research Centre of Natural Sciences.
“On the statistical distribution of prime numbers, a view from the distribution of prime numbers is not erratic.“
-Kristyan’s Equation 2 m= 2(2ab+a+b)+1 where a>b, he shows generates a Set of prime and non-prime odd-composite numbers, with a lot of work on proofs about numbers.
Appendix 3
z
References
A038510 OEIS Composite numbers with smallest prime factor >= 7.
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Appendix 4
My point about the shape of the duplicated numbers in the spreadsheet producing a graph shape exactly the same as that below describing gravitational field (rotate the graph by 90 degrees).
The gravitational field inside the planet is the straight line graph and the field moving away from the planet is the curved line graph.
R = radius
g = gravitational field
z
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