exploring the undesigned
intelligence of the numberverse
NEW The Magic Square of Subtraction: Part 1 - A 'Classic Discovery' Part 2 - A Deterministic Test Part 3 - Semiprimes are in P
It began a few weeks ago with an exploration of biquadratic paired primes: 2 primes separated by the equivalent of exactly 2 quadratic intervals.... Now the investigation has been 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
What are Biquadratic Paired Primes?
Two "new" rules of perfect squares
Does the quadratic interval signify the probability of prime number occurrence? It appears that way. 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 and surprisingly consistent wave form for primes and prime factors.
Try it yourself...!
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.
What is a "perfect prime polynomial"?
What is polynomial pronic alignment?
The high primality of prime-derived quadratic sequences
Use an Excel spreadsheet to explore polynomial primes!
The inspiration for this site...
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New Tools for Testing Natural Numbers |
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All tools are digitally signed for security. |
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MinusSquare: A New Factoring Algorithm (beta) |
The magic square of subtraction has given birth to a baby factoring algorithm. (An explanation to be published soon.) The interesting question is how P is it...? Whether or not it will scale is still a matter for the Investigation.... Download Program (25KB) Show Me |
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Miller-Rabin Demo (with source code ) (beta) |
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Desktop program and complete project source code for what is possibly the only available Visual Basic (VB6) implementation of the gold standard in primality testing. A fast and reliable test for numbers up to 1027-1 (that's 1 with 26 9s - a prime number...!). Download Project (10KB) Download Program (17KB) Show Me |
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FermaticTest (beta) |
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"Fermatic" is a made-up word: Fermat + Automatic. This tool takes Fermat's great theorem and tries to make it "P and NP", with some experiments to weed out pesky pseudoprimes. Rapidly generate prime, pseudoprime, and composite data. |
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QTest (beta) |
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Enter 3 or 4 numbers in a sequence and find out what the next 10, next 1,000, or next 10,000 values are. QTest lets you derive a quadratic equation from the values you input (and solve the equation's roots). Then you can use this polynomial to generate and analyze long number sequences for primality. (See Robert Sacks' method for quadratic derivation, used in Vortex.) Download (35KB) How to Use QTest |
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RadiusTest (beta) |
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Calculates prime and composite distribution in the Sacks Number Spiral by offset (curved series) and angle (straight series). |
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ZetaTest (beta) |
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Real number zeta calculator (includes prime, factorial, and Fibonacci series). Demonstrates the calculation of many important constants - including e, pi, and phi, the Basel equality and Apéry's constant - using infinite series. |
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PrimeTest (beta) |
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Prime and composite number calculator (includes composite analyzer and prime number generator). |
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Dedicated Number Generators for...
The first 1,000,000...
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About the implicate order of natural numbers...