The research
Ten lines of work from June to September 2025, in the order I explored them. Every script, notebook and figure is on GitHub, with a note on what it does and what it really showed.
Prime wave sieve
The founding idea: every small prime sends out a "wave" that peaks on its multiples. Add the waves and the primes are the nodes where the sum is zero. The numbered series (prime01 … prime22) is the original order of experiments. detectors/ holds the 2 Aug class-based detectors, unified-theory-crt/ the 3 Aug versions with Chinese-Remainder "suppression waves", and notebooks/ the write-ups and proof attempts.
What it showed. The wave is exactly the Sieve of Eratosthenes. With context primes up to P it is correct on [1, P²] and nowhere beyond. Every "100%" result used primes up to √N, which is trial division, so the O(1) claims do not hold.
Open the folder on GitHubPhysics-inspired wave models
Lorenz attractors driven by prime frequencies, quantum-style standing waves, radial waves on spirals, and the scripts that produced the matching figures.
What it showed. Visually rich; none of these predicts primes beyond the data they were tuned on.
Open the folder on GitHubComplex plane
The complex-number work: Z(n) = Σ_{p|n} e^{i p ln n} placing primes on the unit circle, spiral trajectories and a fitted differential equation, convergence iterations, "infinite convergence", wobbling (Sacks) and galactic (golden-angle) spirals, plus GPU sieves and a 2^300000 prime hunt.
What it showed. Z(n) has |Z| = 1 for primes and for every prime power (the notebook says so itself). The wobbling spiral is the Sacks spiral and the galactic one is golden-angle phyllotaxis; their reported separations call isprime(n) inside the wave value.
Open the folder on GitHubBit-pair sequences
Primes written as bit pairs ([6k−1 prime], [6k+1 prime]) or ([10k+1 prime], [10k+3 prime]), turned into binary fractions, and fed to recurrences suggested by GPT and Gemini.
What it showed. Both AI recurrences reproduce the 100 pairs they were fit to and then score 24–25% on new pairs, below the 47% of always guessing (0, 0). Berlekamp–Massey shows no short linear rule exists.
Open the folder on GitHubHex sequence puzzle
A 782-character hex string (FA57A5BA4F24D856…) analysed by grouping, pattern search, extension, XOR tests, a middle-square generator, and Conway's Game of Life. day11-…/ keeps the day's original order (01 … 11).
What it showed. The middle-square generator matches the string for only 9 characters, and the 0x1010101 group check matches 0 of 130 groups.
Open the folder on GitHubPrime music
Primes turned into MIDI: gaps as melodic intervals, digits as rhythms, factorisations as chords, golden-ratio spirals, and the hex "Nexus decoder". Generated songs are in midi/.
What it showed. A creative sonification; the web app has a playable version of the gap-interval approach.
Open the folder on GitHubGaps, walks and spirals
Prime gap statistics, factorisation graphs, additive-basis graphs, and the large day-18 folder: functions on a "prime plane", radial spirals, 2D/3D walks, animations and sonified videos. Inside day18 the scripts keep their original v-numbers (v01 … v79) and the output folders keep their names because the scripts write to them.
What it showed. Real phenomena with known explanations: gaps divisible by 6 dominate (Hardy–Littlewood), and radial "webs" show Dirichlet's theorem on primes in progressions.
Open the folder on GitHubMachine learning
Transformers, neural nets, GPU benchmarks, and the day-19 nth-prime work (datasets, regression, gplearn symbolic regression, evaluation, HTML visualisers). Day-19 scripts keep their original numbers as prefixes.
What it showed. Models learn the density of primes, not their positions. The evolved formula is −1.14% at n = 10⁵; Cipolla's textbook formula is −0.017%.
Open the folder on GitHubPrime matrix
Numbers 1 … N² in an N × N grid with composites zeroed, and the eigenvalues of that matrix.
What it showed. Even and odd N differ because of parity: for even N every even column is empty apart from the 2, so half the eigenvalues are 0.
Open the folder on GitHubFactorials and Gamma
Continuous and weighted factorials through the Gamma function, positive and negative arguments.
What it showed. Γ(s/2) is the factor that links ζ(s) and ζ(1 − s) in the functional equation, so this is the right neighbour of the zeta work.
Open the folder on GitHubUse the code
The mathematics from the film is packaged as primewaves for Python and JavaScript: the sieve, the prime wave, Z(n), complex zeta and gamma, the first 1,000 zeta zeros, Riemann's explicit formula and Robin's inequality.
Latest releaseContact
Write to me at joycemalik14@gmail.com, or open a discussion on GitHub.