Block #476,990

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/6/2014, 4:46:00 AM · Difficulty 10.4763 · 6,339,332 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

3b2b518b327848951bc4e85293ed3a7c4cd04d521dba6eae3aed1966694b1cdb

View on Chainz ↗

Height

#476,990

Difficulty

10.476309

Transactions

Size

208 B

Version

Bits

0a79ef67

Nonce

168,477,483

Timestamp

4/6/2014, 4:46:00 AM

Confirmations

6,339,332

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

cf50e7cc99ba6737ca49e5d0a12f5ae17e4bf3fa9f660f585650ee9428b3cb3f

Transactions (1)

Coinbasecf50e7cc99ba67…50ee9428b3cb3f

1 in → 1 out9.1000 XPM116 B

AbwWkWZt…kawDhufa

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.

8.372 × 10⁹⁹(100-digit number)

83729494028523344928…34236813747137326081

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

8.372 × 10⁹⁹(100-digit number)

83729494028523344928…34236813747137326081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.674 × 10¹⁰⁰(101-digit number)

16745898805704668985…68473627494274652161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.349 × 10¹⁰⁰(101-digit number)

33491797611409337971…36947254988549304321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.698 × 10¹⁰⁰(101-digit number)

66983595222818675942…73894509977098608641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.339 × 10¹⁰¹(102-digit number)

13396719044563735188…47789019954197217281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.679 × 10¹⁰¹(102-digit number)

26793438089127470377…95578039908394434561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.358 × 10¹⁰¹(102-digit number)

53586876178254940754…91156079816788869121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.071 × 10¹⁰²(103-digit number)

10717375235650988150…82312159633577738241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.143 × 10¹⁰²(103-digit number)

21434750471301976301…64624319267155476481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.286 × 10¹⁰²(103-digit number)

42869500942603952603…29248638534310952961

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 #476,990

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