Number Theory

   

An Original Method to Find Probable Prime Numbers

Authors: David Hill, Silvio Gabbianelli

This paper presents an original method devised by David Hill for identifying probable prime numbers through a series of systematic steps involving division and rounding. The method begins with selecting any natural number, repeatedly dividing it by 2 until the result ends in a decimal of .5. Based on the parity of the original number, the resulting decimal is then rounded to the nearest even or odd number. This rounded number is either added to or subtracted from the original input number, often resulting in a prime number. While the method does not guarantee a prime in every case, it demonstrates a high success rate, particularly within the range of 2 to 100. An exception is made for generating the prime number 2 from the input number 1. To validate this method, two Python programs were utilized. One program tested integer numbers within a given range one by one, and the other produced a list of probable prime numbers found. Analysis of the results revealed that the method consistently found a higher number of primes than initially estimated. For example, starting in the range of 2 to 100 integers, the method found 34 primes compared to the estimated 25. This pattern held true across larger ranges, with the method finding up to 46.06% more primes out of the estimated in the range of 2 to 10,000,000.Additionally, the method identified the greatest prime numbers that extended significantly beyond the initial range limits. The trend line for the percentage increase in found primes suggested that the method becomes increasingly effective at identifying additional primes as the range expands. These findings suggest that the method has the potential to uncover a greater number of prime numbers than traditional estimation methods predict, providing a new approach to prime number discovery. This could indicate a deeper connection between composite numbers and primes through systematic division and balancing of odds and evens. Further research is needed to determine the method's effectiveness across larger and more varied ranges, but the initial results are promising.[Note: Silvio Gabbianelli created Python programs to test the method. This paper, written by him for me to present. The tests, conducted up to 10,000,000, yielded promising results.]

Comments: 36 Pages. Distributed under Creative Commons Attribution-NoDerivatives 4.0 License

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[v1] 2024-07-26 21:05:40

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