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Block #222,789

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/22/2013, 11:38:44 AM Β· Difficulty 9.9396 Β· 6,603,812 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c67be62a0e06ddf101796e4563e5a89bae48cb211c3c26ee3ee46d12e2de67b7
View on Chainz β†—

Height

#222,789

Difficulty

9.939585

Transactions

1

Size

207 B

Version

2

Bits

09f088a6

Nonce

83,886,431

Timestamp

10/22/2013, 11:38:44 AM

Confirmations

6,603,812

Merkle Root

761ce9e2367b2a6044f25bf655114da9d47863705318f4d1c692a802d505d2ea
Transactions (1)
Coinbase761ce9e2367b2a…92a802d505d2ea
1 in β†’ 1 out10.1100 XPM116 B
AcLBm5Z9…S683d7c3
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.

8.209 Γ— 10⁹⁷(98-digit number)
82097368769135515168…57431230644985174240
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
8.209 Γ— 10⁹⁷(98-digit number)
82097368769135515168…57431230644985174241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.641 Γ— 10⁹⁸(99-digit number)
16419473753827103033…14862461289970348481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.283 Γ— 10⁹⁸(99-digit number)
32838947507654206067…29724922579940696961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.567 Γ— 10⁹⁸(99-digit number)
65677895015308412134…59449845159881393921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.313 Γ— 10⁹⁹(100-digit number)
13135579003061682426…18899690319762787841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.627 Γ— 10⁹⁹(100-digit number)
26271158006123364853…37799380639525575681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.254 Γ— 10⁹⁹(100-digit number)
52542316012246729707…75598761279051151361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.050 Γ— 10¹⁰⁰(101-digit number)
10508463202449345941…51197522558102302721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.101 Γ— 10¹⁰⁰(101-digit number)
21016926404898691883…02395045116204605441
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 222789

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 c67be62a0e06ddf101796e4563e5a89bae48cb211c3c26ee3ee46d12e2de67b7

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 #222,789 on Chainz β†—
Circulating Supply:57,856,960 XPMΒ·at block #6,826,600 Β· updates every 60s
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