Block #324,712

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/22/2013, 12:50:32 PM · Difficulty 10.2069 · 6,474,201 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

f81d2a68b35b76e6c47d981d72ab9def25a8da6c5901bbb9199457eb891c091f

View on Chainz ↗

Height

#324,712

Difficulty

10.206864

Transactions

Size

1.08 KB

Version

Bits

0a34f50e

Nonce

230,004

Timestamp

12/22/2013, 12:50:32 PM

Confirmations

6,474,201

Mined by

⛏️ haRAQ8QAT3JKsV1xD6zC94z9djnpJrCFKuVbR

Merkle Root

b03e8e40591db69ab7ccbe6ea141d83dd7edbe469c9c7e7cf9af97a682473bb8

Transactions (1)

Coinbaseb03e8e40591db6…af97a682473bb8

1 in → 28 out9.5600 XPM1015 B

AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz Aac9Hjdg…P4ktypc3 AG5YAjec…VhA4Aeh1 Ac6mGvmQ…XqWmPHjR

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.

1.844 × 10⁹⁷(98-digit number)

18446110606110774124…76314810458465530881

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

1.844 × 10⁹⁷(98-digit number)

18446110606110774124…76314810458465530881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.689 × 10⁹⁷(98-digit number)

36892221212221548248…52629620916931061761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.378 × 10⁹⁷(98-digit number)

73784442424443096496…05259241833862123521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.475 × 10⁹⁸(99-digit number)

14756888484888619299…10518483667724247041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.951 × 10⁹⁸(99-digit number)

29513776969777238598…21036967335448494081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.902 × 10⁹⁸(99-digit number)

59027553939554477197…42073934670896988161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.180 × 10⁹⁹(100-digit number)

11805510787910895439…84147869341793976321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.361 × 10⁹⁹(100-digit number)

23611021575821790878…68295738683587952641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.722 × 10⁹⁹(100-digit number)

47222043151643581757…36591477367175905281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

9.444 × 10⁹⁹(100-digit number)

94444086303287163515…73182954734351810561

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