Block #280,940

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/28/2013, 8:43:54 PM · Difficulty 9.9758 · 6,528,839 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a6ab3705a2198b035db8d2b9ee358d38ab94ace197e21ebb10fffe365c462c2f

View on Chainz ↗

Height

#280,940

Difficulty

9.975804

Transactions

Size

1.18 KB

Version

Bits

09f9ce47

Nonce

24,679

Timestamp

11/28/2013, 8:43:54 PM

Confirmations

6,528,839

Mined by

⛏️ lIaR%QAc6mGvmQ9ya8dQxqWNQYGz81U4XqWmPHjR

Merkle Root

d9f05f68f730acb7555747991f472b3a1ade05b7aba1de72425d8d7ce3ead6c9

Transactions (1)

Coinbased9f05f68f730ac…5d8d7ce3ead6c9

1 in → 31 out10.0100 XPM1.09 KB

Ac6mGvmQ…XqWmPHjR AWGQhzDN…RDYvugUy ATePXsVW…RySkxuH3 ALw8WzMm…sj2uYfgL AMbCuLHZ…WSoStwkc

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.

3.167 × 10⁹³(94-digit number)

31670904911348223516…69194292135962167281

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

3.167 × 10⁹³(94-digit number)

31670904911348223516…69194292135962167281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.334 × 10⁹³(94-digit number)

63341809822696447032…38388584271924334561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.266 × 10⁹⁴(95-digit number)

12668361964539289406…76777168543848669121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.533 × 10⁹⁴(95-digit number)

25336723929078578812…53554337087697338241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.067 × 10⁹⁴(95-digit number)

50673447858157157625…07108674175394676481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.013 × 10⁹⁵(96-digit number)

10134689571631431525…14217348350789352961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.026 × 10⁹⁵(96-digit number)

20269379143262863050…28434696701578705921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.053 × 10⁹⁵(96-digit number)

40538758286525726100…56869393403157411841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.107 × 10⁹⁵(96-digit number)

81077516573051452201…13738786806314823681

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 #280,940

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