Project Euler Hard Problems Encode NP-Complete Graph Structures — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Project Euler's "hard" problems (PE#60 prime pair sets, PE#61 cyclic figurate numbers) reduce to graph-theoretic and NP-complete structures, revealing that prime/figurate number relationships encode combinatorial graphs | MATH: PE#60: find minimal prime set {p₁...p₅} where all pairwise concatenations pᵢpⱼ and pⱼpᵢ are prime — equivalent to finding minimum-weight clique K₅ in a graph G where vertices = primes, edges = concatenation-primality predicate. PE#61: find cyclic set of 6 figurate numbers (triangular Tₙ=n(n+1)/2, square n², pentagonal n(3n−1)/2, hexagonal n(2n−1), heptagonal n(5n−3)/2, octagonal n(3n−2)) where last 2 digits of each = first 2 digits of next, forming a Hamiltonian cycle in a directed graph | CONNECTION: Figurate numbers derive from polygonal geometry — the general formula P(s,n) = [(s−2)n² − (s−4)n]/2 encodes crystallographic polygon symmetries. The 6-fold cyclic constraint in PE#61 maps to hexagonal lattice symmetry (6-fold rotational symmetry, C₆). Prim Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225270104
Cites:
Cited by:
Related to: