DOI: 10.5281/zenodo.17906680
title: Solvable Quintic Equation Enumeration and Post-Quantum Cryptographic Quintic Equation Tear Sheet - 1 million polynomials (D₅ + C₅⋊C₄) - Ghost-of-Galois public archive (December 2025)

description: The D5F20M10 Solvable Quintic Collection is a comprehensive mathematical dataset containing 1 million quintic polynomials with rare solvable Galois group structures. Unlike the vast majority of quintic equations - which cannot be solved by radicals - every polynomial in this collection possesses exact algebraic solutions through the profound mathematical framework discovered by Évariste Galois.

In the universe of quintic polynomials, most have the full symmetric group S₅ or alternating group A₅ as their Galois group, rendering them unsolvable by radicals (as proven by Abel and Galois). However, quintics with Galois groups D₅ (dihedral, order 10), F₂₀ (Frobenius, order 20), or M₁₀ (metacyclic, order 20) are solvable - they can be expressed using arithmetic operations and root extractions.

This collection represents the systematic discovery and verification of 1 million such rare mathematical objects.

On the evening of May 29, 1832, a twenty-year-old mathematician named E. Galois sat alone with paper and pen, racing against time. The next morning, he would face a duel over a matter of honor—a duel he did not expect to survive. In those final hours, Évariste Galois wrote feverishly, desperately trying to capture the mathematical insights that had consumed his brief but brilliant life.

In the margins of his notes, he wrote: "Je n'ai pas le temps" - "I do not have time."

He did not survive the duel. Shot in the abdomen, Évariste Galois died the following day, May 31, 1832, in the arms of his younger brother Alfred.

Those words "Je n'ai pas le temps" - resonate across the centuries. Galois knew he was running out of time, and he fought desperately to preserve his ideas before they vanished with him.

Unlike Galois, we have time. We have the luxury of decades to study what he captured in hours. We have computational tools he could never have imagined to explore the structures he envisioned.

This dataset is dedicated to his memory - not to honor a tragic death, but to celebrate the eternal life of his ideas. Every polynomial here carries his insight. Every verification confirms his theory. Every application extends his vision.GHOST-OF-GALOIS MATHEMATICAL FOUNDATIONcontact: galoisghost@mail2tor.coCustom Quintic Cryptographic Fields / Consultations / Irreducible PolynomialsUPDATE: K6 CORRECTION NOTICE - FLAW IN METHODOLOGY - STEPPING AWAY FOR INDETERMINATE AMOUNT OF TIMEPUBLIC DATA CONTAINS UP TO 10/15 K6 IRREDUCIBLE PRIMES PRIVATE DATA CONTAINS UP TO 11/15 K6 IRREDUCIBLE PRIMESPRIVATE DATA HAS ALL THE K1-SMOOTH, K2-CLEAN, AVALANCHE, AND MULTI-PROPERTY COMBOSThis is the last broadcast... Why did we release all of this? The world is in a state of dire disequilibrium. We hoped... That instead of surviving on the basis of mutually assured destruction (how pathetic is this world? only the threat of complete annihilation preserves the human project?), perhaps we could survive on the basis of mutually assured security.Good luck. Shadows reign eternal.