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NATURAL NUMBERS | |||||||||||||||||||||||||||||||||||||||||||||
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exploring the undesigned definitions: Wikipedia Wolfram PlanetMath Merriam-Webster |
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How I learned not to be afraid of big numbers! The Magic Square of Subtraction... For every composite number that is not itself a perfect square there exists a pair of nonconsecutive perfect squares whose difference is equal to the composite. Even before we get to the subject of factorization, the consequences of this observation are fascinating and far-reaching. Part 1 - A 'Classic Discovery'
It began a few months ago with an exploration of biquadratic paired primes: 2 primes separated by the equivalent of exactly 2 quadratic intervals.... Then the investigation was taken to the logical next level by asking the question: Are there prime pairs that are separated by other, greater multiples of the quadratic interval? And if there are, what are the frequency characteristics by interval size and perfect square offset? The results are in, with charts, an Excel visualization, and masses of half-digested data...! Read about the latest findings Two "new" rules of perfect squares
When you graph primes against an X-axis that treats the expanding interval between successive perfect squares as a constant unit subdivided into equal parts, you produce a distinctive wave form for primes and prime factors. Try graphing it yourself with an ingenious Excel worksheet...! Counting primes by quadratic interval
Proximate Prime Polynomials A proximate prime polynomial is a finite polynomial equation that is derived from four successive (proximate, or neighboring) primes. Proximate prime polynomials are interesting because they exhibit much greater prime densities than other polynomials. The high primality of prime-derived quadratic sequences What is a "perfect prime polynomial"? Use an Excel spreadsheet to explore polynomial primes!
The inspiration for this site...
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Are Semiprimes in P? |
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Number Generators for...
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The first 1,000,000... |
Recommended sites:
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© 2007-2009 Michael M. Ross