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Block #222,452

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/22/2013, 6:14:54 AM Β· Difficulty 9.9394 Β· 6,572,891 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
240c0cfcbc40e377c55e45bdf3971ec178ee5234c78d061edea9f268fd5c2715
View on Chainz β†—

Height

#222,452

Difficulty

9.939406

Transactions

1

Size

200 B

Version

2

Bits

09f07ce3

Nonce

92,630

Timestamp

10/22/2013, 6:14:54 AM

Confirmations

6,572,891

Merkle Root

927aaf51b348da9f079b2ba55f148e4c58b3c36be6080c2dd75b045440672f4d
Transactions (1)
Coinbase927aaf51b348da…5b045440672f4d
1 in β†’ 1 out10.1100 XPM110 B
AbuU1HhS…JPwsJEbB
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.851 Γ— 10⁹⁴(95-digit number)
78514293310386448102…17957006250074842000
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 1

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.

1
origin βˆ’ 1
7.851 Γ— 10⁹⁴(95-digit number)
78514293310386448102…17957006250074841999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.570 Γ— 10⁹⁡(96-digit number)
15702858662077289620…35914012500149683999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.140 Γ— 10⁹⁡(96-digit number)
31405717324154579240…71828025000299367999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.281 Γ— 10⁹⁡(96-digit number)
62811434648309158481…43656050000598735999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.256 Γ— 10⁹⁢(97-digit number)
12562286929661831696…87312100001197471999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.512 Γ— 10⁹⁢(97-digit number)
25124573859323663392…74624200002394943999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.024 Γ— 10⁹⁢(97-digit number)
50249147718647326785…49248400004789887999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.004 Γ— 10⁹⁷(98-digit number)
10049829543729465357…98496800009579775999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.009 Γ— 10⁹⁷(98-digit number)
20099659087458930714…96993600019159551999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin β€” the large number shown above β€” 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 β†’
β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9
How Primecoin's Proof-of-Work Constructs These Primes

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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Verify on a Primecoin Node

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.

1. Get block hash by height
getblockhash 222452

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 240c0cfcbc40e377c55e45bdf3971ec178ee5234c78d061edea9f268fd5c2715

Returns 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 β†’ Debug Window β†’ 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.

View Block #222,452 on Chainz β†—
Circulating Supply:57,606,796 XPMΒ·at block #6,795,342 Β· updates every 60s
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