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Preliminary Construction Proof of Prime Numbers having a cubic nature!
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"Construction" Proof Relevance
Aside from the elementary summing , there are no equations involved except a simple curve fit thar extrapolates to higher estimates in order to show that the running sum of the Prime Numbers using Lp, the Golden Ratio logs, continues indefinitely, in an obviously orderly manner.
The simplicity of the proof and its graphs should allow for an opinion
of correctness at least; significance can be dealt with later out of fairness to the Data presented which can be re-generated on any computer, by simply summing the PN's upward and recording the STEP,PN,SUM trio at unit Lp thresholds.
Geometry: Graphs and Methods
1. Chose a volume amount; assign it to that of a Dodecahedron ;
2. Compute the Dodecahedron's EDGE value from ( Volume / 7.66312 )^-3 ; its Height or Width was its Edge times the Square root of 5.
3. The Lp of the EDGE value is the Top Plane value and the Area index for the face.
4. A Tone volume is geometrically a 12th of the dodecahedron's volume; it was made of layers of Vections corresponding to the step pattern labeled in the table by Top Plane / EDGE values.
---------- Since the Volume of a Dodecahedron equals "12 * PNsum" , thus making its EDGE equal to (12 / 7.66312 * PNsum )^-3 !
5. For example, at step 2342 the sum is 22.802509e6, multiplying it by "12 / 7.66312 " gives a volume of 35.70740705e6 ,
its cube root is 329.2957342~ which translates to an 12.0465789~ Top Plane value which is more accurate than the estimate derived from just using the last three sums. Note that the sum in this case is also Prime.
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05Jan2011