Learn About Prime Numbers
Explore the mathematics, cryptography, and history behind Primecoin's proof-of-work — from Fermat's primality tests to the largest primes ever discovered. Each article is written to be accessible without sacrificing mathematical depth.
Primecoin & Cryptography
How prime chains power real-world security
Every block mined by Primecoin discovers a Cunningham chain containing safe primes — the same mathematical structures used in TLS, SSH, and Diffie-Hellman key exchange. Explore the deep connection between Primecoin's proof-of-work and the foundations of modern cryptography.
Prime Chain Applications
1CC, 2CC, and bi-twin chains explained
What makes a Cunningham chain of the first kind different from the second? Why are bi-twin chains so extraordinarily rare? This article breaks down the three chain types Primecoin discovers, their mathematical significance, and why longer chains are exponentially harder to find.
The Mathematics of Discovery
Fermat tests, primality proofs, and difficulty
How does a miner know a number is prime without spending hours on a full proof? Primecoin uses a two-stage probabilistic test combining Fermat's Little Theorem with the Euler-Lagrange-Lifchitz method — fast enough for mining, rigorous enough for mathematics.
Historical Prime Records
From Cataldi in 1588 to 41 million digits in 2024
The search for ever-larger prime numbers spans four centuries, from Pietro Cataldi's hand calculations to GIMPS's distributed computing network. Discover where Primecoin fits into this grand tradition — and why Cunningham chains represent a fundamentally different kind of prime record.
Blockchain & Proof of Work
Why Primecoin's mining is different
Bitcoin miners burn electricity computing meaningless hashes. Primecoin miners solve a genuine mathematical problem with lasting scientific value. This article examines the concept of Proof of Useful Work, how Primecoin achieves it, and why the design is both elegant and secure.