Starting Point: Trial Division

The most obvious approach: for every number n, check if any integer from 2 to √n divides it evenly.

def is_prime(n):
    if n < 2:
        return False
    for i in range(2, int(n**0.5) + 1):
        if n % i == 0:
            return False
    return True

Simple, but slow for large ranges. Every number gets its own full check.

The Sieve of Eratosthenes

Instead of checking one number at a time, the Sieve marks composites in bulk:

def sieve(limit):
    is_prime = [True] * (limit + 1)
    is_prime[0] = is_prime[1] = False
    for i in range(2, int(limit**0.5) + 1):
        if is_prime[i]:
            for j in range(i*i, limit + 1, i):
                is_prime[j] = False
    return [i for i, v in enumerate(is_prime) if v]

This is dramatically faster for finding all primes up to a large limit, but requires memory proportional to the limit.

Taking It Further: A Cluster

For very large ranges, I set up a small network of computers to split the work. Each machine handled a segment of the number range, and results were collected centrally.

The honest finding: for ranges where everything fits in memory, a well-optimized local sieve beats the cluster. Network overhead and coordination costs hurt small jobs. But the cluster showed its value for ranges too large for any single machine’s RAM.

What I Took Away

• Algorithm choice matters more than raw hardware, up to a point
• Distributed computing has real overhead that has to be justified by the problem size
• Benchmarking with real numbers (not assumptions) is essential

I’m planning to explore segmented sieves and possibly GPU-based approaches next.

This site is where I document the projects I’m working on, write about things I’m learning, and keep a public record of my work in engineering, software, and athletics.

What you’ll find here

• Projects — writeups of technical projects from school and on my own time
• Blog — short posts on topics I’m exploring: algorithms, hardware, design thinking, and more
• Resume — my academic resume and athletic profile

What I’m working on

Right now I’m taking AP Computer Science A, AP Calculus, and AP Psychology while competing in outdoor Track & Field — currently ranked 10th in Class 3A in the 3200m. On the technical side, I’ve been experimenting with distributed computing, and I’m planning to go deeper into systems programming and cybersecurity.

Check back as I add more — this site is a work in progress, just like everything else.