Tim
Varley
Principal Systems Engineer & Technical Lead specializing in distributed systems, AI-driven development, and high-performance infrastructure.
Featured Projects
AI-Native IoT Platform
AI-native IoT platform optimizing water and energy consumption with distributed sensor networks, built entirely using advanced LLM agents.
B2B E-commerce Marketplace
Cloud-native B2B e-commerce platform disrupting the promotional products industry with extreme scalability and 20% cost optimization.
Enterprise SaaS Migration
Transformed legacy monolithic software into cloud-native microservices architecture, achieving 170% performance boost and 99.9% uptime.
High-Frequency Financial Infrastructure
Mission-critical financial data infrastructure delivering embargoed government economic releases to trading systems in under 15 milliseconds.
FinTech Patent Solution
Pioneering multi-channel banking system architecture that earned a US patent and Smithsonian Innovation Award for bridging legacy and digital banking.
AI-Native Portfolio & Blog
A high-performance personal platform built 100% via autonomous AI agents, directed by senior engineering architectural patterns. Demonstrates the power of experience-driven agentic workflows.
AI-Generated Euler Solutions
A repository of 50+ mathematical algorithm solutions generated entirely by AI agents. Showcases how deep engineering expertise guides AI to produce optimal, mathematically rigorous code.
Recent Solutions
View All →Consecutive Prime Sum
The prime $41$, can be written as the sum of six consecutive primes: $$41 = 2 + 3 + 5 + 7 + 11 + 13.$$ This is the longest sum of consecutive primes that adds to a prime below one-hundred. The longest sum of consecutive primes below one-thousand that adds to a prime, contains $21$ terms, and is equal to $953$. Which prime, below one-million, can be written as the sum of the most consecutive primes?
Prime Permutations
The arithmetic sequence, $1487, 4817, 8147$, in which each of the terms increases by $3330$, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the $4$-digit numbers are permutations of one another. There are no arithmetic sequences made up of three $1$-, $2$-, or $3$-digit primes, exhibiting this property, but there is one other $4$-digit increasing sequence. What $12$-digit number do you form by concatenating the three terms in this sequence?
Self Powers
The series, $1^1 + 2^2 + 3^3 + \cdots + 10^{10} = 10405071317$. Find the last ten digits of the series, $1^1 + 2^2 + 3^3 + \cdots + 1000^{1000}$.
Distinct Primes Factors
The first two consecutive numbers to have two distinct prime factors are: - 14 = 2 × 7 - 15 = 3 × 5 The first three consecutive numbers to have three distinct prime factors are: - 644 = 2² × 7 × 23 - 645 = 3 × 5 × 43 - 646 = 2 × 17 × 19 Find the first four consecutive integers to have four distinct prime factors each. What is the first of these numbers?
Goldbach's Other Conjecture
It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square. - 9 = 7 + 2 × 1² - 15 = 7 + 2 × 2² - 21 = 3 + 2 × 3² - 25 = 7 + 2 × 3² - 27 = 19 + 2 × 2² - 33 = 31 + 2 × 1² It turns out that the conjecture was false. What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
Triangular, Pentagonal, and Hexagonal
Triangle, pentagonal, and hexagonal numbers are generated by the following formulae: Triangle: T_n = n(n+1)/2, sequence: 1, 3, 6, 10, 15, ... Pentagonal: P_n = n(3n-1)/2, sequence: 1, 5, 12, 22, 35, ... Hexagonal: H_n = n(2n-1), sequence: 1, 6, 15, 28, 45, ... It can be verified that T285 = P165 = H143 = 40755. Find the next triangle number that is also pentagonal and hexagonal.