Block #249,585

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/8/2013, 1:13:25 AM · Difficulty 9.9671 · 6,548,548 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

6fbf27f9ca8a62ef74e7823c4e1b934b5e7345f56c65f8a065602d5749e1ed2d

View on Chainz ↗

Height

#249,585

Difficulty

9.967080

Transactions

Size

2.27 KB

Version

Bits

09f7928f

Nonce

59,447

Timestamp

11/8/2013, 1:13:25 AM

Confirmations

6,548,548

Mined by

⛏️ R|:$ANo4YY1xjeppLPNm9kAdtJjYCnvnsPRDSU

Merkle Root

bfc7ea364f71ef281db184199b52a695b69d4963bafac5d756e40e54b157c736

Transactions (1)

Coinbasebfc7ea364f71ef…e40e54b157c736

1 in → 64 out10.0200 XPM2.19 KB

ANo4YY1x…vnsPRDSU AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY AJzWx2VD…j4ZSMit5 ARR7aRH6…ne3DXGXZ

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.

1.443 × 10⁹⁵(96-digit number)

14431862988506479134…10933739508823715681

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

1.443 × 10⁹⁵(96-digit number)

14431862988506479134…10933739508823715681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.886 × 10⁹⁵(96-digit number)

28863725977012958269…21867479017647431361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.772 × 10⁹⁵(96-digit number)

57727451954025916539…43734958035294862721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.154 × 10⁹⁶(97-digit number)

11545490390805183307…87469916070589725441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.309 × 10⁹⁶(97-digit number)

23090980781610366615…74939832141179450881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.618 × 10⁹⁶(97-digit number)

46181961563220733231…49879664282358901761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.236 × 10⁹⁶(97-digit number)

92363923126441466463…99759328564717803521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.847 × 10⁹⁷(98-digit number)

18472784625288293292…99518657129435607041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.694 × 10⁹⁷(98-digit number)

36945569250576586585…99037314258871214081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.389 × 10⁹⁷(98-digit number)

73891138501153173170…98074628517742428161

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