Block #31,650
2CCLength 8★☆☆☆☆Cunningham Chain of the Second Kind · Discovered 7/14/2013, 12:11:52 AM · Difficulty 7.9891 · 6,759,975 confirmations
A sequence where each prime is double the previous prime minus one.
Height
#31,650
Difficulty
7.989063
Transactions
2
Size
359 B
Version
2
Bits
07fd333c
Nonce
131
Timestamp
7/14/2013, 12:11:52 AM
Confirmations
6,759,975
Merkle Root
This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.
These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.
What this block proved
The miner who found this block proved the existence of 8 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.
Found in most blocks. The baseline for Primecoin's proof-of-work.
Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.
This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula: