Building a Distributed Prime Number Finder: Scalable Sieve Architecture for 1 Billion Integers

#systemdesign #algorithms #mathematics #kubernetes

🧮 From Math to Distributed Systems: Scaling Prime Number Computation

What if you had to find every prime number up to 1,000,000,000 — but couldn’t use a single machine? This isn’t just a number theory problem anymore. At this scale, it becomes a distributed computing challenge. In this deep-dive, we design a production-grade system that transforms the classic Segmented Sieve of Eratosthenes into a parallel, fault-tolerant, and memory-optimized architecture. 💡 We break down how to slice the number space into stateless computation segments, broadcast base primes efficiently, and distribute work across compute clusters — all while ensuring retry safety, deterministic output, and high throughput.

🖥️ Cloud-Native, Observable, and Battle-Tested

This isn’t just a theoretical model. We show how to bring it to life using real-world distributed principles: REST APIs for job submission 🚀, distributed task queues like Kafka/Redis for dispatch 📬, and stateless compute workers running in Kubernetes or Ray 🧠. The final output aggregation is streaming-friendly, memory-safe, and extensible to S3, HDFS, or parquet stores 📦. Whether you're building on Spark, Ray, or just containers and queues, this article gives you an end-to-end reference implementation with code walkthroughs, database schemas, retry logic, and observability patterns via Prometheus/Grafana 📊. If you love distributed system design and want to see algorithm meets architecture — this post is for you.