The Distribution of Prime Numbers on the Square Root Spiral
- Harry K. Hahn -
Ludwig-Erhard-Str. 10 D-76275 EtGermanytlingen, Germany
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contribution from “ The Number Spiral “ by
- Robert Sachs -
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30. June 2007
Abstract :
Prime Numbers accumulate on defined spiral graphs, which run through the Square Root Spiral. These spiral graphs can be assigned to different spiral-systems, in which all spiral-graphs have the same direction of rotation and the same “second difference” between the numbers, which lie on these spiral-graphs. A mathematical analysis shows, that these spiral-graphs are caused exclusively by quadratic polynomials. For example the well known Euler Polynomial x2+x+41 appears on the Square Root Spiral in the form of three spiral-graphs, which are defined by three different quadratic polynomials.
All natural numbers, divisible by a certain prime factor, also lie on defined spiral graphs on the Square Root Spiral ( or “Spiral of Theodorus”, or “Wurzelspirale” ). And the Square Numbers 4, 9, 16, 25, 36 … even form a highly three-symmetrical system of three spiral graphs, which divides the square root spiral into three equal areas. Fibonacci number sequences also play a part in the structure of the Square Root Spiral. To learn more about these amazing facts, see my detailed introduction to the Square Root Spiral :