Block #306,594

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/12/2013, 3:18:04 AM · Difficulty 9.9939 · 6,487,026 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

5b31f39cec371c684581d220ce5c0d4c833b5d4fc1b020c7ef26dad383b051e5

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Height

#306,594

Difficulty

9.993938

Transactions

Size

1.21 KB

Version

Bits

09fe72b6

Nonce

10,596

Timestamp

12/12/2013, 3:18:04 AM

Confirmations

6,487,026

Merkle Root

29e17704b984b3e471618891a7782a08a085c6674b4670c93013382f8466bd67

Transactions (1)

Coinbase29e17704b984b3…13382f8466bd67

1 in → 32 out9.9800 XPM1.12 KB

Ae58nAEb…GFUA15fv AcC2zSod…rtWatH79 AXmS7tZu…11YypHLP ASLwCAXH…njQM8ENK AaD5wr9W…eU2RcM2H

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.

1.453 × 10⁹⁷(98-digit number)

14532016687006917128…40122732034109857281

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

1.453 × 10⁹⁷(98-digit number)

14532016687006917128…40122732034109857281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.906 × 10⁹⁷(98-digit number)

29064033374013834256…80245464068219714561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.812 × 10⁹⁷(98-digit number)

58128066748027668512…60490928136439429121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.162 × 10⁹⁸(99-digit number)

11625613349605533702…20981856272878858241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.325 × 10⁹⁸(99-digit number)

23251226699211067405…41963712545757716481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.650 × 10⁹⁸(99-digit number)

46502453398422134810…83927425091515432961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.300 × 10⁹⁸(99-digit number)

93004906796844269620…67854850183030865921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.860 × 10⁹⁹(100-digit number)

18600981359368853924…35709700366061731841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.720 × 10⁹⁹(100-digit number)

37201962718737707848…71419400732123463681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.440 × 10⁹⁹(100-digit number)

74403925437475415696…42838801464246927361

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