Block #475,173

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/5/2014, 1:34:29 AM · Difficulty 10.4564 · 6,324,301 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

18745534c500a93a9d2e9c049aa8fadb38da74160c2a7d067b8fe33032bbf078

View on Chainz ↗

Height

#475,173

Difficulty

10.456439

Transactions

Size

902 B

Version

Bits

0a74d92b

Nonce

40,481

Timestamp

4/5/2014, 1:34:29 AM

Confirmations

6,324,301

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

1d8f394bd61398af5f48e2375f0418ab218fc4a2998959da1ecb18a0bf1c63c4

Transactions (1)

Coinbase1d8f394bd61398…cb18a0bf1c63c4

1 in → 22 out9.1300 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AUFKXvnz…342ApNcm AMW1p9oT…2TzdaZxH AUDD9tmA…gJPQLnsz

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.

1.284 × 10⁹⁷(98-digit number)

12848942146285184184…93408723969619680481

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

1.284 × 10⁹⁷(98-digit number)

12848942146285184184…93408723969619680481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.569 × 10⁹⁷(98-digit number)

25697884292570368368…86817447939239360961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.139 × 10⁹⁷(98-digit number)

51395768585140736737…73634895878478721921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.027 × 10⁹⁸(99-digit number)

10279153717028147347…47269791756957443841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.055 × 10⁹⁸(99-digit number)

20558307434056294694…94539583513914887681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.111 × 10⁹⁸(99-digit number)

41116614868112589389…89079167027829775361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.223 × 10⁹⁸(99-digit number)

82233229736225178779…78158334055659550721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.644 × 10⁹⁹(100-digit number)

16446645947245035755…56316668111319101441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.289 × 10⁹⁹(100-digit number)

32893291894490071511…12633336222638202881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.578 × 10⁹⁹(100-digit number)

65786583788980143023…25266672445276405761

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