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Block #186,637

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/30/2013, 12:34:46 AM Β· Difficulty 9.8671 Β· 6,618,466 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b75b954f565e4e761d469ba7e533ea74552efee638b54bed7174682d4eebde2b
View on Chainz β†—

Height

#186,637

Difficulty

9.867086

Transactions

1

Size

200 B

Version

2

Bits

09ddf961

Nonce

34,882

Timestamp

9/30/2013, 12:34:46 AM

Confirmations

6,618,466

Merkle Root

93dac73f3484c21525129951bce3e98fb5bfc784c5e6606ddea53238bf2b4fd4
Transactions (1)
Coinbase93dac73f3484c2…a53238bf2b4fd4
1 in β†’ 1 out10.2600 XPM110 B
ANvtpRa1…QjsraDJz
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.

1.218 Γ— 10⁹⁡(96-digit number)
12184179603357229687…72360443014037644800
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
1.218 Γ— 10⁹⁡(96-digit number)
12184179603357229687…72360443014037644801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.436 Γ— 10⁹⁡(96-digit number)
24368359206714459374…44720886028075289601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.873 Γ— 10⁹⁡(96-digit number)
48736718413428918748…89441772056150579201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.747 Γ— 10⁹⁡(96-digit number)
97473436826857837497…78883544112301158401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.949 Γ— 10⁹⁢(97-digit number)
19494687365371567499…57767088224602316801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.898 Γ— 10⁹⁢(97-digit number)
38989374730743134999…15534176449204633601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.797 Γ— 10⁹⁢(97-digit number)
77978749461486269998…31068352898409267201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.559 Γ— 10⁹⁷(98-digit number)
15595749892297253999…62136705796818534401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.119 Γ— 10⁹⁷(98-digit number)
31191499784594507999…24273411593637068801
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 186637

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 b75b954f565e4e761d469ba7e533ea74552efee638b54bed7174682d4eebde2b

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 #186,637 on Chainz β†—
Circulating Supply:57,684,891 XPMΒ·at block #6,805,102 Β· updates every 60s
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