Prime Chain Visualizations
Mathematical patterns and distributions in Primecoin's proof-of-work discoveries.
Chain Type Distribution
Proportion of each prime chain type discovered
- Bi-Twin
- Cunningham 1st
- Cunningham 2nd
Chain Length Distribution
How many primes are in each discovered chain
Daily Discovery Timeline
Prime chains discovered per day by type (last 30 days)
- Cunningham 1st
- Cunningham 2nd
- Bi-Twin
Chain Length Over Recent Blocks
How chain length varies across the most recent 300 blocks
Mathematical Significance
Primecoin's proof-of-work is the first cryptocurrency mining algorithm to produce results of genuine scientific value. Rather than computing arbitrary hash functions, miners search for Cunningham chains and bi-twin chains — rare sequences of prime numbers studied in number theory.
A Cunningham chain of the first kind starting at prime p takes the form:
Each prime in a Cunningham chain is a safe prime— a prime of the form 2q+1 where q is also prime (a Sophie Germain prime). These have important applications in cryptography, particularly in Diffie-Hellman key exchange protocols.
The longer the chain, the rarer and more mathematically significant the discovery. Chains of length 7 or more are exceptionally rare and represent genuine contributions to our knowledge of prime number distributions.