exploring the undesigned
intelligence of the numberverse

lists/generators: Perfect Squares, Composites, Primes

"...out all day long.
All day long,
it goes on and on"

The First 1,000,000...

Lists of Composites

Generate Your Own Up to 1027...

Perfect Square Generator

Prime Factors Generator

Prime Generator

Experimental Calculators

Secrets of the Spiral

Proximate-Prime Polynomials

A proximate-prime polynomial is simply a quadratic equation - a finite polynomial of the second degree - 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!

Catch the Wave...

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 out an ingenious Excel worksheet to see the wave!

Fixing Fermat’s Factorization Method

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.

Q-Paired Primes...

It began with an exploration of biquadratic paired primes: 2 primes separated by the equivalent of exactly 2 quadratic intervals.... Then the investigation took 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...!

Two "new" rules of perfect squares

How I learned not to be afraid of big numbers

It's a question of magnitude...

Using Excel as a tool for number theory

Find examples throughout this site that demonstrate using VBA code with worksheets and graphing - including generating primes, perfect squares, and composites, doing modular arithmetic, calculating GCDs, and more....

 Tools for Testing Natural Numbers MinusSquare Miller-Rabin FermaticTest QTest RadiusTest ZetaTest PrimeTest

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Divisor Plot

Interesting Graphing Applets