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Block #181,854

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/26/2013, 8:52:11 PM Β· Difficulty 9.8601 Β· 6,645,501 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eca29b402dbb2fff24299db1e412f085befa9c7a210d2b2dc3887f8207912aff
View on Chainz β†—

Height

#181,854

Difficulty

9.860064

Transactions

1

Size

206 B

Version

2

Bits

09dc2d26

Nonce

16,777,919

Timestamp

9/26/2013, 8:52:11 PM

Confirmations

6,645,501

Merkle Root

bac4dcee9f1488ccafd53b67dfc6a1086d9565fcf1c8aae2855d09053d441919
Transactions (1)
Coinbasebac4dcee9f1488…5d09053d441919
1 in β†’ 1 out10.2700 XPM117 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.

5.858 Γ— 10⁹¹(92-digit number)
58588958806648250610…45124899862620384000
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
5.858 Γ— 10⁹¹(92-digit number)
58588958806648250610…45124899862620384001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.171 Γ— 10⁹²(93-digit number)
11717791761329650122…90249799725240768001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.343 Γ— 10⁹²(93-digit number)
23435583522659300244…80499599450481536001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.687 Γ— 10⁹²(93-digit number)
46871167045318600488…60999198900963072001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.374 Γ— 10⁹²(93-digit number)
93742334090637200976…21998397801926144001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.874 Γ— 10⁹³(94-digit number)
18748466818127440195…43996795603852288001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.749 Γ— 10⁹³(94-digit number)
37496933636254880390…87993591207704576001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.499 Γ— 10⁹³(94-digit number)
74993867272509760781…75987182415409152001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.499 Γ— 10⁹⁴(95-digit number)
14998773454501952156…51974364830818304001
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 181854

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 eca29b402dbb2fff24299db1e412f085befa9c7a210d2b2dc3887f8207912aff

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 #181,854 on Chainz β†—
Circulating Supply:57,862,938 XPMΒ·at block #6,827,354 Β· updates every 60s
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