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Block #9,371

1CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/10/2013, 10:11:13 PM Β· Difficulty 7.6169 Β· 6,798,477 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
477bc529bc5196d5de3a9fd353c27008a8d587943f6a8b781eca0ca0f5c3a789
View on Chainz β†—

Height

#9,371

Difficulty

7.616934

Transactions

1

Size

198 B

Version

2

Bits

079def6a

Nonce

504

Timestamp

7/10/2013, 10:11:13 PM

Confirmations

6,798,477

Merkle Root

449c4050d51e916201ef815646d5845b199b1c3296aa00e7f06eaa03fca55521
Transactions (1)
Coinbase449c4050d51e91…6eaa03fca55521
1 in β†’ 1 out17.2100 XPM109 B
AdWHv8yo…8LoH1JaP
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.

5.419 Γ— 10⁹¹(92-digit number)
54194834032047027682…62087184300191412750
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
5.419 Γ— 10⁹¹(92-digit number)
54194834032047027682…62087184300191412749
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.083 Γ— 10⁹²(93-digit number)
10838966806409405536…24174368600382825499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.167 Γ— 10⁹²(93-digit number)
21677933612818811073…48348737200765650999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.335 Γ— 10⁹²(93-digit number)
43355867225637622146…96697474401531301999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.671 Γ— 10⁹²(93-digit number)
86711734451275244292…93394948803062603999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.734 Γ— 10⁹³(94-digit number)
17342346890255048858…86789897606125207999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.468 Γ— 10⁹³(94-digit number)
34684693780510097717…73579795212250415999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 consecutive prime numbers forming a Cunningham Chain of the First 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 7
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 9371

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 477bc529bc5196d5de3a9fd353c27008a8d587943f6a8b781eca0ca0f5c3a789

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 #9,371 on Chainz β†—
Circulating Supply:57,706,823 XPMΒ·at block #6,807,847 Β· updates every 60s
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