Block #475,442

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/5/2014, 6:00:12 AM · Difficulty 10.4565 · 6,333,458 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

0cffe21905d81c8bc698b769b2409518d25f6b011ae348fe0da11239eb3ec172

View on Chainz ↗

Height

#475,442

Difficulty

10.456532

Transactions

Size

202 B

Version

Bits

0a74df4a

Nonce

77,810

Timestamp

4/5/2014, 6:00:12 AM

Confirmations

6,333,458

Mined by

⛏️ P2SHAR6arNiMwpePFYEQCcEhPVjxwPHUa2VqVg

Merkle Root

daf842b35cde443dfc37364478cd54e886d33480d073a9a0f6ce70cff5cc5b6e

Transactions (1)

Coinbasedaf842b35cde44…ce70cff5cc5b6e

1 in → 1 out9.1300 XPM110 B

AR6arNiM…HUa2VqVg

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.

1.153 × 10¹⁰⁰(101-digit number)

11539924356892501770…66793383443849825281

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

1.153 × 10¹⁰⁰(101-digit number)

11539924356892501770…66793383443849825281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.307 × 10¹⁰⁰(101-digit number)

23079848713785003541…33586766887699650561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.615 × 10¹⁰⁰(101-digit number)

46159697427570007082…67173533775399301121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.231 × 10¹⁰⁰(101-digit number)

92319394855140014164…34347067550798602241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.846 × 10¹⁰¹(102-digit number)

18463878971028002832…68694135101597204481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.692 × 10¹⁰¹(102-digit number)

36927757942056005665…37388270203194408961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.385 × 10¹⁰¹(102-digit number)

73855515884112011331…74776540406388817921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.477 × 10¹⁰²(103-digit number)

14771103176822402266…49553080812777635841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.954 × 10¹⁰²(103-digit number)

29542206353644804532…99106161625555271681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.908 × 10¹⁰²(103-digit number)

59084412707289609065…98212323251110543361

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

Block #475,442

Cookie Preferences