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Block #186,660

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/30/2013, 1:04:52 AM Β· Difficulty 9.8670 Β· 6,608,206 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8cc341c4a8445e10dacb15801442e1a6e24046466eeba4ea245bb4b14dc971d3
View on Chainz β†—

Height

#186,660

Difficulty

9.866965

Transactions

1

Size

197 B

Version

2

Bits

09ddf165

Nonce

603,583

Timestamp

9/30/2013, 1:04:52 AM

Confirmations

6,608,206

Merkle Root

05fb3bd6168fff50aedc857241488b1bf93429d2991dc223d29679ed192a388d
Transactions (1)
Coinbase05fb3bd6168fff…9679ed192a388d
1 in β†’ 1 out10.2600 XPM109 B
ATK4r8Gh…Usic4A9N
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.

4.846 Γ— 10⁸⁹(90-digit number)
48463461207282760038…84111876286497065950
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
4.846 Γ— 10⁸⁹(90-digit number)
48463461207282760038…84111876286497065951
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.692 Γ— 10⁸⁹(90-digit number)
96926922414565520077…68223752572994131901
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.938 Γ— 10⁹⁰(91-digit number)
19385384482913104015…36447505145988263801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.877 Γ— 10⁹⁰(91-digit number)
38770768965826208030…72895010291976527601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.754 Γ— 10⁹⁰(91-digit number)
77541537931652416061…45790020583953055201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.550 Γ— 10⁹¹(92-digit number)
15508307586330483212…91580041167906110401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.101 Γ— 10⁹¹(92-digit number)
31016615172660966424…83160082335812220801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.203 Γ— 10⁹¹(92-digit number)
62033230345321932849…66320164671624441601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.240 Γ— 10⁹²(93-digit number)
12406646069064386569…32640329343248883201
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 186660

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 8cc341c4a8445e10dacb15801442e1a6e24046466eeba4ea245bb4b14dc971d3

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 #186,660 on Chainz β†—
Circulating Supply:57,602,960 XPMΒ·at block #6,794,865 Β· updates every 60s
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