Unlimited Numbers

Explore primes, sequences, and number systems.

Mac iPhone iPad

On the Mac App Store now. iPhone and iPad coming soon.

Start with one number and follow it outward. Unlimited Numbers connects the number line, primes, fractions, sequences, the complex plane, finite fields, infinity, and the structures between them in one native playground.

One number, everything it knows

• Fly along the number line — move through negative integers, zero, primes, squares, fractions, and familiar constants, then zoom out until the thinning of the primes becomes visible.
• Open its card — see an integer’s factorisation, divisor lattice, arithmetic functions, nearby primes, and every named property that applies to it.
• Follow the source — property definitions and mathematical claims carry references you can check.
• Keep one value in hand — move the same integer, fraction, decimal, exact constant, or Gaussian integer between rooms without starting over.

See the structure behind arithmetic

• Watch primes take shape — explore Ulam, Sacks, and Vogel spirals, prime gaps, counting functions, residue races, and the Goldbach comet.
• Turn algebra into geometry — draw modular multiplication as chords, the Chinese remainder theorem as a wrapping grid, and continued fractions as rectangles cut by Euclid’s algorithm.
• Walk between fractions — browse Farey sequences, the Stern–Brocot tree, Ford circles, Egyptian fractions, and the best rational approximations.
• Work with large integers — factor up to 120 digits within an eight-second on-device budget, or test primality up to 1,000 digits.

Go past the familiar line

• See what a decimal really is — inspect floating-point values exactly, recognize constants and algebraic numbers, and study repeating expansions in any base.
• Feel complex multiplication — move points directly and watch multiplication rotate and scale them; then explore Gaussian integers and the primes of the complex plane.
• Enter other number systems — p-adic numbers, finite fields, number fields, ordinals, cardinals, surreals, and the algebras beyond the complex numbers.
• Look toward the frontier — plot the critical line of the zeta function and draw families of algebraic numbers as the roots of integer polynomials.

Explore, play, and teach

• The map places the natural numbers inside the integers, rationals, reals, and complex numbers, with guided tours through the ideas that connect them.
• Named sequences come with their terms, plots, definitions, and reasons they matter.
• Games hide the answer while keeping the app’s real mathematical machinery underneath.
• Printable worksheets include computed answer keys for factorisation, sieves, fractions, Euclid’s algorithm, and modular arithmetic.

One purchase, every device