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Block #54,380

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/16/2013, 8:08:54 PM · Difficulty 8.9329 · 6,755,794 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

5a0afa16833432333e1c347c29e3d0e2ab3816dfc32e4cd53d1e4b09cd1ed06b

View on Chainz ↗

Height

#54,380

Difficulty

8.932855

Transactions

Size

210 B

Version

Bits

08eecf9e

Nonce

748

Timestamp

7/16/2013, 8:08:54 PM

Confirmations

6,755,794

Merkle Root

028f0d36f4e2eb5ca19fe28656d8d962c90c6c1a56f4626f44ed095a904390f6

Transactions (1)

Coinbase028f0d36f4e2eb…ed095a904390f6

1 in → 1 out12.5100 XPM110 B

AXY6feyt…oghmWWGf

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.

5.013 × 10¹¹⁸(119-digit number)

50137197591306966567…18964251411209327010

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

5.013 × 10¹¹⁸(119-digit number)

50137197591306966567…18964251411209327011

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.002 × 10¹¹⁹(120-digit number)

10027439518261393313…37928502822418654021

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.005 × 10¹¹⁹(120-digit number)

20054879036522786626…75857005644837308041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.010 × 10¹¹⁹(120-digit number)

40109758073045573253…51714011289674616081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.021 × 10¹¹⁹(120-digit number)

80219516146091146507…03428022579349232161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.604 × 10¹²⁰(121-digit number)

16043903229218229301…06856045158698464321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.208 × 10¹²⁰(121-digit number)

32087806458436458603…13712090317396928641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.417 × 10¹²⁰(121-digit number)

64175612916872917206…27424180634793857281

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 54380

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 5a0afa16833432333e1c347c29e3d0e2ab3816dfc32e4cd53d1e4b09cd1ed06b

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 #54,380 on Chainz ↗

Block #54,380

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