Block #449,330

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/18/2014, 12:45:31 PM · Difficulty 10.3719 · 6,345,720 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

5c5fde0f55eb956c743f4538cf7af46db8436a909b16e390300d86d2518658fa

View on Chainz ↗

Height

#449,330

Difficulty

10.371890

Transactions

Size

360 B

Version

Bits

0a5f3430

Nonce

243,434

Timestamp

3/18/2014, 12:45:31 PM

Confirmations

6,345,720

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

2fb27445955ce3d0c0ac6418531aae6bc00920462465730d2dbb67cb3b6421ef

Transactions (2)

Coinbase328ba68d182f28…55b0c4aef3d3c3

1 in → 1 out9.2900 XPM110 B

AeKNrjNj…1NEq95Ta

92557ce1eaed21…48fa698e4eca2c

1 in → 1 out9.3100 XPM157 B

ATV4M1CV…dd9zw8nH

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.

1.788 × 10¹⁰¹(102-digit number)

17883271515363697678…05108705234041352321

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

1.788 × 10¹⁰¹(102-digit number)

17883271515363697678…05108705234041352321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.576 × 10¹⁰¹(102-digit number)

35766543030727395357…10217410468082704641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.153 × 10¹⁰¹(102-digit number)

71533086061454790715…20434820936165409281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.430 × 10¹⁰²(103-digit number)

14306617212290958143…40869641872330818561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.861 × 10¹⁰²(103-digit number)

28613234424581916286…81739283744661637121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.722 × 10¹⁰²(103-digit number)

57226468849163832572…63478567489323274241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.144 × 10¹⁰³(104-digit number)

11445293769832766514…26957134978646548481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.289 × 10¹⁰³(104-digit number)

22890587539665533028…53914269957293096961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.578 × 10¹⁰³(104-digit number)

45781175079331066057…07828539914586193921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

9.156 × 10¹⁰³(104-digit number)

91562350158662132115…15657079829172387841

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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, …

Cross-reference on Chainz Explorer