exploring the undesigned
intelligence of the numberverse
definitions: Wikipedia Wolfram PlanetMath Merriam-Webster
How I learned not to be afraid of big numbers!
It's a question of magnitude....
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'
Part 2 - A Deterministic Test
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
What are Biquadratic Paired Primes?
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"?
What is polynomial pronic alignment?
Use an Excel spreadsheet to explore polynomial primes!
The inspiration for this site...
Are Semiprimes in P?
Instantly factor a semiprime!
Reveal the DNA of semiprimes
The Q square of factoring
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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: 26-Apr-08) |
The magic square of subtraction has given birth to a baby factoring algorithm. Download Program (25KB) Show Me |
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Miller-Rabin Demo with source code (beta: 2-Feb-08) |
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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: 23-Jan-08) |
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"Fermatic" is a made-up word: Fermat + Automatic. This tool takes Fermat's great theorem to the limit, with some experiments to weed out pesky pseudoprimes. Rapidly generate prime, pseudoprime, and composite data. |
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QTest (beta: 21-Jul-08) |
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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: 23-Jan-08) |
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Calculate prime and composite distribution in the Sacks Number Spiral by offset (curved series) and angle (straight series). |
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ZetaTest (beta: 4-Feb-08) |
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Calculate the products of infinite series using almost any inputs you can think of. Generates real number zeta series, demonstrating the calculation of many important constants - including e, pi, and phi, the Basel equality and Apéry's constant. |
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PrimeTest (beta: 23-Jan-08) |
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Prime and composite number calculator (with prime and nonprime factor analyzer and prime number generator). |
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Number Generators for...
The first 1,000,000...
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