Block #263,804

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/18/2013, 3:38:20 AM · Difficulty 9.9655 · 6,540,391 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e8d371ceb8554b1dd74668aa9f7d593c5a8e5401322c8a88bd7b6f5932a2c772

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Height

#263,804

Difficulty

9.965483

Transactions

Size

1.78 KB

Version

Bits

09f729e3

Nonce

30,426

Timestamp

11/18/2013, 3:38:20 AM

Confirmations

6,540,391

Mined by

⛏️ |aRATaiAP5CNeTYrcp775AJmapQ3Vo4tqgUvu

Merkle Root

47134c3c378e0e5eb96bab3492e63931925f298caffdc03e7ecb669c46c52d79

Transactions (1)

Coinbase47134c3c378e0e…cb669c46c52d79

1 in → 49 out10.0300 XPM1.69 KB

ATaiAP5C…o4tqgUvu AQtzUSwq…htAuF3yC APZy8y6E…QZaGQjfp AFxYnWJi…bUMAd5Gt AHTdyorL…HDnqyrkM

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.

1.565 × 10⁹³(94-digit number)

15654848699656966092…56909014773747900161

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

1.565 × 10⁹³(94-digit number)

15654848699656966092…56909014773747900161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.130 × 10⁹³(94-digit number)

31309697399313932185…13818029547495800321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.261 × 10⁹³(94-digit number)

62619394798627864371…27636059094991600641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.252 × 10⁹⁴(95-digit number)

12523878959725572874…55272118189983201281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.504 × 10⁹⁴(95-digit number)

25047757919451145748…10544236379966402561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.009 × 10⁹⁴(95-digit number)

50095515838902291497…21088472759932805121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.001 × 10⁹⁵(96-digit number)

10019103167780458299…42176945519865610241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.003 × 10⁹⁵(96-digit number)

20038206335560916598…84353891039731220481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.007 × 10⁹⁵(96-digit number)

40076412671121833197…68707782079462440961

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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