John D. Cook

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Posts

Race between primes of the forms 4k + 1 and 4k + 3

Wagon’s algorithm in Python

Finding a square root of -1 mod p

Finding a non-square mod p

Expressing a prime as the sum of two squares

Aligning one matrix with another

Computing large Fibonacci numbers

Fibonacci numbers and time-space tradeoffs

Minimum of cosine sum

Eigenvalue homework problems are backward

Fibonacci number certificates

Γ(1/n)

Polish serenity

Satellites have a lot of room

AGI, ASI, A*I – Do we have all we need to get there?

Bridging secrets is hard

Fortunes and Geometric Means

Proving you know a product

How to prove you know a discrete logarithm

Mills ratio and tail thickness

Sigmas and Student

Stylometry

Two cheers for ugly code

Prime gaps and Gapcoin

Prime clusters

Efficiently testing multiple primes at once

Tighter bounds in the prime number theorem

Efficiently computing multiple modular inverses at once

The middle binomial coefficient

Combining in-shuffles and out-shuffles

Primecoin primality test

Bi-twin prime chains

Prime chains

Compressing a set of hash values

Memorizing chemical element symbols

Largest known compositorial prime

log2(3) and log2(5)

In-shuffles and out-shuffles

Perfect and imperfect shuffles

Knight’s tour with fewest obtuse angles

The center of the earth is not straight down

Interesting categories are big

Klein bottle

Automation and Validation

When was Newton born?

Mason, Dixon, and Latitude

Bowie integrator and the nonlinear pendulum

Trying to fit exponential data

Trying to fit a logistic curve

Regular expressions that cross lines

Multiples with no large digits

Golden iteration

Just change the key

Rolling n-sided dice to get at least n

Weak derivatives

Fourier transform of a Fourier series

Fourier transform of a flat line

Obscuring P2P nodes with Dandelion

What is a Pedersen commitment?

Solving spherical triangles

The Navigational Triangle

Line of position (LOP)

Lewis & Clark geolocation

Zero knowlege proof of compositeness

Monero subaddresses

A triangle whose interior angles sum to zero

A circle in the hyperbolic plane

Equal things that don’t look equal

Hyperbolic metric

TV tuned to a dead channel

How stealth addresses work in Monero

Weddle integration rule

Solving H_n = 100

Closest harmonic number to an integer

Closest consecutive reciprocal sum to an integer

Pythagorean triples

RSA as a pairing

Three-party Diffie-Hellman in one shot

Elliptic curve pairings in cryptography

Adding an imaginary unit to a finite field

Four generalizations of the Pythagorean theorem

Elementary symmetric polynomials and optimization

Weighting an average to minimize variance

Brownian motion and Riemann zeta

Rolling correlation

Analog of Heron’s formula on a sphere

How much is a gigawatt?

Japanese polygon theorem

Tetrahedral analog of the Pythagorean theorem

The anti-Smith chart

Impedance and Trianglular Numbers

Cross ratio

Text case changes the size of QR codes

An ancient generalization of the Pythagorean theorem

Mentally compute logs base 2

Physical Keys and Encryption Keys

Freshman’s dream

Why and how Bitcoin uses Merkle trees

How blocks are chained in a blockchain

987654321 / 123456789

Spacing the circles on the Smith chart

The Smith chart

Generating random points in Colorado

Random spherical coordinates

Distribution of correlation

Distribution of coordinates on a sphere

ODE to Fisher’s transform

Quality metrics

Turning trig identities into Fibonacci identities

Experiences with GPT-5-Codex

Ethereum’s consensus layer elliptic curve

Inverting matrices and bilinear functions

Generate random points inside a sphere

Random samples from a tetrahedron

GPT-5 for AI-assisted discovery