Cunningham Chain of the First Kind Ā· Discovered 12/26/2013, 2:55:18 AM Ā· Difficulty 10.1686 Ā· 6,513,676 confirmations
A sequence where each prime is double the previous prime plus one.
Height
#329,634
Difficulty
10.168559
Transactions
1
Size
1.08 KB
Version
2
Bits
0a2b26b2
Nonce
180,283
Timestamp
12/26/2013, 2:55:18 AM
Confirmations
6,513,676
Merkle Root
This is the prime chain origin stored in the block header. It is a composite number (not prime itself) ā 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 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin ā the large number shown above ā anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.
View full Prime Chain Discovery page āPrimecoin 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 Ć 3 Ć 5 Ć 7 Ć ā¦), the result is the first prime in the chain. The origin is deliberately divisible by this primorial ā that divisibility is part of the proof.
This is why the origin has many small prime factors ā those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:
Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.
getblockhash 329634Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.
getblock 553d37bef2e7a592f477cb74f1b56151521f327cc15efa0c44f87a9657c8faa4Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.
How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help ā Debug Window ā Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.
Cross-reference on Chainz Explorer
Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.