Block #263,720

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/18/2013, 1:56:50 AM · Difficulty 9.9656 · 6,531,927 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

59d711a66eeafcb92fb800741f181039580c09b3e45a92a22dc1c76e82526ff8

View on Chainz ↗

Height

#263,720

Difficulty

9.965596

Transactions

Size

1.84 KB

Version

Bits

09f73148

Nonce

54,973

Timestamp

11/18/2013, 1:56:50 AM

Confirmations

6,531,927

Mined by

⛏️ aRsAdWEcK3rEzi97mdrbQ1dKgt3GmHNaeWgVb

Merkle Root

31c11e0b265dfd6ac22eb9d5803323a5487274786259f11c71f539e9d8a7e20a

Transactions (1)

Coinbase31c11e0b265dfd…f539e9d8a7e20a

1 in → 51 out10.0300 XPM1.75 KB

AdWEcK3r…HNaeWgVb AHUMdCV5…eXnCsijo APfZjrNu…Wvzt6AFp AQtzUSwq…htAuF3yC ANHbaxZp…XjnHCJJs

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.

9.432 × 10⁹⁴(95-digit number)

94327841140225528221…52885201255860064641

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

9.432 × 10⁹⁴(95-digit number)

94327841140225528221…52885201255860064641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.886 × 10⁹⁵(96-digit number)

18865568228045105644…05770402511720129281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.773 × 10⁹⁵(96-digit number)

37731136456090211288…11540805023440258561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.546 × 10⁹⁵(96-digit number)

75462272912180422577…23081610046880517121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.509 × 10⁹⁶(97-digit number)

15092454582436084515…46163220093761034241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.018 × 10⁹⁶(97-digit number)

30184909164872169030…92326440187522068481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.036 × 10⁹⁶(97-digit number)

60369818329744338061…84652880375044136961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.207 × 10⁹⁷(98-digit number)

12073963665948867612…69305760750088273921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.414 × 10⁹⁷(98-digit number)

24147927331897735224…38611521500176547841

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