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Block #15,423

1CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/11/2013, 7:27:52 PM Β· Difficulty 7.8516 Β· 6,794,120 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5b9609d338c3bcb59bf540fbbbd56c44f1e8e6eef9fa496ab539e9de92dc361d
View on Chainz β†—

Height

#15,423

Difficulty

7.851597

Transactions

1

Size

203 B

Version

2

Bits

07da024a

Nonce

261

Timestamp

7/11/2013, 7:27:52 PM

Confirmations

6,794,120

Merkle Root

e1b23249f59d80064040cb378a904a605c0fad914a00679688e88ddac916f59d
Transactions (1)
Coinbasee1b23249f59d80…e88ddac916f59d
1 in β†’ 1 out16.2000 XPM108 B
ALtQiCyn…68VU6xPK
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.

3.455 Γ— 10¹⁰⁢(107-digit number)
34551432658234515813…72231559115180406000
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
3.455 Γ— 10¹⁰⁢(107-digit number)
34551432658234515813…72231559115180405999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.910 Γ— 10¹⁰⁢(107-digit number)
69102865316469031627…44463118230360811999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.382 Γ— 10¹⁰⁷(108-digit number)
13820573063293806325…88926236460721623999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.764 Γ— 10¹⁰⁷(108-digit number)
27641146126587612650…77852472921443247999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.528 Γ— 10¹⁰⁷(108-digit number)
55282292253175225301…55704945842886495999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.105 Γ— 10¹⁰⁸(109-digit number)
11056458450635045060…11409891685772991999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.211 Γ— 10¹⁰⁸(109-digit number)
22112916901270090120…22819783371545983999
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 15423

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 5b9609d338c3bcb59bf540fbbbd56c44f1e8e6eef9fa496ab539e9de92dc361d

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 #15,423 on Chainz β†—
Circulating Supply:57,720,416 XPMΒ·at block #6,809,542 Β· updates every 60s
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