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Block #267,669

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/21/2013, 11:26:34 AM Β· Difficulty 9.9587 Β· 6,544,786 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e0c9a5aeffd8ee81f798f6d0617c17054d10c4b8052cc5cab9b3cb5ad6af5a22
View on Chainz β†—

Height

#267,669

Difficulty

9.958702

Transactions

1

Size

209 B

Version

2

Bits

09f56d82

Nonce

8,179

Timestamp

11/21/2013, 11:26:34 AM

Confirmations

6,544,786

Merkle Root

43e952cba5942602dff8e5b0793677597c8724eb64791f0cdba4d9e4ea597d1a
Transactions (1)
Coinbase43e952cba59426…a4d9e4ea597d1a
1 in β†’ 1 out10.0700 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.

4.664 Γ— 10¹⁰²(103-digit number)
46640670580169436162…44738646984424396800
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
4.664 Γ— 10¹⁰²(103-digit number)
46640670580169436162…44738646984424396799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.328 Γ— 10¹⁰²(103-digit number)
93281341160338872325…89477293968848793599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.865 Γ— 10¹⁰³(104-digit number)
18656268232067774465…78954587937697587199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.731 Γ— 10¹⁰³(104-digit number)
37312536464135548930…57909175875395174399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.462 Γ— 10¹⁰³(104-digit number)
74625072928271097860…15818351750790348799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.492 Γ— 10¹⁰⁴(105-digit number)
14925014585654219572…31636703501580697599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.985 Γ— 10¹⁰⁴(105-digit number)
29850029171308439144…63273407003161395199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.970 Γ— 10¹⁰⁴(105-digit number)
59700058342616878288…26546814006322790399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.194 Γ— 10¹⁰⁡(106-digit number)
11940011668523375657…53093628012645580799
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 267669

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 e0c9a5aeffd8ee81f798f6d0617c17054d10c4b8052cc5cab9b3cb5ad6af5a22

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 #267,669 on Chainz β†—
Circulating Supply:57,743,664 XPMΒ·at block #6,812,454 Β· updates every 60s
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