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Block #156,883

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2013, 6:17:00 AM Β· Difficulty 9.8688 Β· 6,670,290 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7dbcd38e3de4528c9dd77199a23f470019f920987e2dff0dcabd79c608f5a275
View on Chainz β†—

Height

#156,883

Difficulty

9.868794

Transactions

1

Size

200 B

Version

2

Bits

09de6949

Nonce

49,842

Timestamp

9/9/2013, 6:17:00 AM

Confirmations

6,670,290

Merkle Root

6c9f3fb97b133fc1cd2a33410316a538b9cc9dcb6d321394013be62affa3b8dc
Transactions (1)
Coinbase6c9f3fb97b133f…3be62affa3b8dc
1 in β†’ 1 out10.2500 XPM109 B
AKUegfDd…wwHBC13P
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.

2.001 Γ— 10⁹⁢(97-digit number)
20013651537217682813…11421781143541837600
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
2.001 Γ— 10⁹⁢(97-digit number)
20013651537217682813…11421781143541837601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.002 Γ— 10⁹⁢(97-digit number)
40027303074435365626…22843562287083675201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.005 Γ— 10⁹⁢(97-digit number)
80054606148870731253…45687124574167350401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.601 Γ— 10⁹⁷(98-digit number)
16010921229774146250…91374249148334700801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.202 Γ— 10⁹⁷(98-digit number)
32021842459548292501…82748498296669401601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.404 Γ— 10⁹⁷(98-digit number)
64043684919096585002…65496996593338803201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.280 Γ— 10⁹⁸(99-digit number)
12808736983819317000…30993993186677606401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.561 Γ— 10⁹⁸(99-digit number)
25617473967638634001…61987986373355212801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.123 Γ— 10⁹⁸(99-digit number)
51234947935277268002…23975972746710425601
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 156883

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 7dbcd38e3de4528c9dd77199a23f470019f920987e2dff0dcabd79c608f5a275

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 #156,883 on Chainz β†—
Circulating Supply:57,861,481 XPMΒ·at block #6,827,172 Β· updates every 60s
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