Euler's Hidden Depths: Strategies for Select Problems, Not Hardest Solutions — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Project Euler problems reveal algorithmic elegance in number theory, but the specific "hardest" solutions are not disclosed in these videos — only problem-solving strategies for select problems (1, 23, 40, 50, and a cyclic figurate problem). MATH: - Problem 50: Consecutive prime sums — involves prime counting function π(x), partial sums, and the Riemann hypothesis as a *performance* bound (not a proof requirement). - Problem 40: Champernowne's constant — 0.123456789101112... — digit extraction via arithmetic progression; no closed-form constant beyond the base-10 concatenation. - Problem 23: Abundant numbers — sum of proper divisors σ(n) > 2n; the limit for non-abundant sums is 28123 (known bound). - Cyclic figurate numbers: polygonal numbers (triangular P₃(n)=n(n+1)/2, square P₄(n)=n², pentagonal P₅(n)=n(3n−1)/2, hexagonal P₆(n)=n(2n−1), heptagonal P₇(n)=n(5n−3)/2, octagonal P₈(n)=n(3n−2)) — cyclic sets require digit-matching (last two digits = first two digits of 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: W7212322371
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