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Block #185,096

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/29/2013, 1:47:36 AM Β· Difficulty 9.8623 Β· 6,629,923 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
df9439871f1286de46d0b89cff8d83a85341a8a9d3e4679718aaeee5ec07517c
View on Chainz β†—

Height

#185,096

Difficulty

9.862257

Transactions

1

Size

201 B

Version

2

Bits

09dcbcd8

Nonce

58,093

Timestamp

9/29/2013, 1:47:36 AM

Confirmations

6,629,923

Merkle Root

7eb887b3e65f7d35933d7ae9691459f6bd068b942e6a26fc8791b7195294391f
Transactions (1)
Coinbase7eb887b3e65f7d…91b7195294391f
1 in β†’ 1 out10.2700 XPM109 B
AcDoNL3w…ViN23bk2
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.

1.993 Γ— 10⁹⁹(100-digit number)
19930247419622683003…53330113606457557600
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
1.993 Γ— 10⁹⁹(100-digit number)
19930247419622683003…53330113606457557601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.986 Γ— 10⁹⁹(100-digit number)
39860494839245366007…06660227212915115201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.972 Γ— 10⁹⁹(100-digit number)
79720989678490732014…13320454425830230401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.594 Γ— 10¹⁰⁰(101-digit number)
15944197935698146402…26640908851660460801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.188 Γ— 10¹⁰⁰(101-digit number)
31888395871396292805…53281817703320921601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.377 Γ— 10¹⁰⁰(101-digit number)
63776791742792585611…06563635406641843201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.275 Γ— 10¹⁰¹(102-digit number)
12755358348558517122…13127270813283686401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.551 Γ— 10¹⁰¹(102-digit number)
25510716697117034244…26254541626567372801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.102 Γ— 10¹⁰¹(102-digit number)
51021433394234068489…52509083253134745601
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 185096

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 df9439871f1286de46d0b89cff8d83a85341a8a9d3e4679718aaeee5ec07517c

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 #185,096 on Chainz β†—
Circulating Supply:57,764,239 XPMΒ·at block #6,815,018 Β· updates every 60s
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