Block #284,718

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/30/2013, 5:35:40 AM · Difficulty 9.9832 · 6,523,231 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a518c94fa12ec71c85b4faf550c2bb9fb6e01cea9fade12deb27b301ca0e8a2a

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Height

#284,718

Difficulty

9.983197

Transactions

Size

1.14 KB

Version

Bits

09fbb2c6

Nonce

6,658

Timestamp

11/30/2013, 5:35:40 AM

Confirmations

6,523,231

Mined by

⛏️ .XaRy=uAbtgNzNbw1hJh3uoaBwXxdpmiY9Atvu81w

Merkle Root

5915ad7a8271271dff341abf08d2a8f67e15f95086c9d1250def4e72f7c6c0e9

Transactions (1)

Coinbase5915ad7a827127…ef4e72f7c6c0e9

1 in → 30 out10.0000 XPM1.06 KB

AbtgNzNb…9Atvu81w Ac5sZcdP…kzV4eckG AGHJDQA6…hCLcZMXq AVYk5NCd…9CZ4Ym8K AJHH6QuE…N3s6fxLC

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.

3.016 × 10⁸⁸(89-digit number)

30167276053479006972…15156338151673154181

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

3.016 × 10⁸⁸(89-digit number)

30167276053479006972…15156338151673154181

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.033 × 10⁸⁸(89-digit number)

60334552106958013944…30312676303346308361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.206 × 10⁸⁹(90-digit number)

12066910421391602788…60625352606692616721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.413 × 10⁸⁹(90-digit number)

24133820842783205577…21250705213385233441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.826 × 10⁸⁹(90-digit number)

48267641685566411155…42501410426770466881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.653 × 10⁸⁹(90-digit number)

96535283371132822311…85002820853540933761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.930 × 10⁹⁰(91-digit number)

19307056674226564462…70005641707081867521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.861 × 10⁹⁰(91-digit number)

38614113348453128924…40011283414163735041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.722 × 10⁹⁰(91-digit number)

77228226696906257849…80022566828327470081

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #284,718

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