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Block #208,182

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/13/2013, 8:59:15 PM Β· Difficulty 9.9054 Β· 6,586,322 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8ab0d8e50c356e8914b696b0efc241bb3e27a9c25e8afb1201613ade2ed7157e
View on Chainz β†—

Height

#208,182

Difficulty

9.905358

Transactions

1

Size

209 B

Version

2

Bits

09e7c58d

Nonce

6,040

Timestamp

10/13/2013, 8:59:15 PM

Confirmations

6,586,322

Merkle Root

a6667fc03cab98b624b7e60844a7265bb84349afb6c5f5d6de6944bdee89cce4
Transactions (1)
Coinbasea6667fc03cab98…6944bdee89cce4
1 in β†’ 1 out10.1800 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.

1.784 Γ— 10¹⁰¹(102-digit number)
17844331110184913084…21501140133991715840
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
1.784 Γ— 10¹⁰¹(102-digit number)
17844331110184913084…21501140133991715839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.568 Γ— 10¹⁰¹(102-digit number)
35688662220369826169…43002280267983431679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.137 Γ— 10¹⁰¹(102-digit number)
71377324440739652339…86004560535966863359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.427 Γ— 10¹⁰²(103-digit number)
14275464888147930467…72009121071933726719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.855 Γ— 10¹⁰²(103-digit number)
28550929776295860935…44018242143867453439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.710 Γ— 10¹⁰²(103-digit number)
57101859552591721871…88036484287734906879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.142 Γ— 10¹⁰³(104-digit number)
11420371910518344374…76072968575469813759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.284 Γ— 10¹⁰³(104-digit number)
22840743821036688748…52145937150939627519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.568 Γ— 10¹⁰³(104-digit number)
45681487642073377497…04291874301879255039
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 208182

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 8ab0d8e50c356e8914b696b0efc241bb3e27a9c25e8afb1201613ade2ed7157e

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 #208,182 on Chainz β†—
Circulating Supply:57,600,067 XPMΒ·at block #6,794,503 Β· updates every 60s
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