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Block #74,147

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/21/2013, 9:40:51 AM · Difficulty 8.9953 · 6,716,912 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

0a38d6580a9e711d42d85b5bcde5a1b50113d62031ba60336c56dabf029c83d0

View on Chainz ↗

Height

#74,147

Difficulty

8.995312

Transactions

Size

204 B

Version

Bits

08feccbe

Nonce

2,482

Timestamp

7/21/2013, 9:40:51 AM

Confirmations

6,716,912

Merkle Root

e4708ef641b7a27b25069e04f8b25bacca4a9b341e4c93077de28d0900d893a8

Transactions (1)

Coinbasee4708ef641b7a2…e28d0900d893a8

1 in → 1 out12.3400 XPM110 B

AXANAczP…aJfm8KN3

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.609 × 10¹⁰⁵(106-digit number)

16095575738436172915…22775688089771265080

Discovered Prime Numbers

p_k = 2^k × 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.

origin + 1

1.609 × 10¹⁰⁵(106-digit number)

16095575738436172915…22775688089771265081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.219 × 10¹⁰⁵(106-digit number)

32191151476872345831…45551376179542530161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.438 × 10¹⁰⁵(106-digit number)

64382302953744691662…91102752359085060321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.287 × 10¹⁰⁶(107-digit number)

12876460590748938332…82205504718170120641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.575 × 10¹⁰⁶(107-digit number)

25752921181497876664…64411009436340241281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.150 × 10¹⁰⁶(107-digit number)

51505842362995753329…28822018872680482561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.030 × 10¹⁰⁷(108-digit number)

10301168472599150665…57644037745360965121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.060 × 10¹⁰⁷(108-digit number)

20602336945198301331…15288075490721930241

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — 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 →

★☆☆☆☆

Rarity

CommonChain length 8

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 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 74147

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 0a38d6580a9e711d42d85b5bcde5a1b50113d62031ba60336c56dabf029c83d0

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 → Debug Window → 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 #74,147 on Chainz ↗