Block #265,497

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/19/2013, 3:07:44 PM · Difficulty 9.9624 · 6,529,377 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

9bb127023712d2c9937642456860004353c1bfedb33c1a760c1ab94bb171377b

View on Chainz ↗

Height

#265,497

Difficulty

9.962427

Transactions

Size

1.84 KB

Version

Bits

09f6619d

Nonce

117,436

Timestamp

11/19/2013, 3:07:44 PM

Confirmations

6,529,377

Mined by

⛏️ aR~NAJ83QDaoSnQQgeKxvuLGszzGf7DqWdAVWo

Merkle Root

a50c6436e5b722bfc118b0aadeb0355939f1e26b0307fa0f92203c578ff7e6d0

Transactions (1)

Coinbasea50c6436e5b722…203c578ff7e6d0

1 in → 51 out10.0400 XPM1.75 KB

AJ83QDao…DqWdAVWo AMttQDuf…7j6tfS9x ANHbaxZp…XjnHCJJs AVzhvfTX…ZzNJYq61 AGPBDvpY…HsUDJ9oq

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.

2.764 × 10⁹⁴(95-digit number)

27640643294182245829…86224002680983161121

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

2.764 × 10⁹⁴(95-digit number)

27640643294182245829…86224002680983161121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.528 × 10⁹⁴(95-digit number)

55281286588364491658…72448005361966322241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.105 × 10⁹⁵(96-digit number)

11056257317672898331…44896010723932644481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.211 × 10⁹⁵(96-digit number)

22112514635345796663…89792021447865288961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.422 × 10⁹⁵(96-digit number)

44225029270691593326…79584042895730577921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.845 × 10⁹⁵(96-digit number)

88450058541383186653…59168085791461155841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.769 × 10⁹⁶(97-digit number)

17690011708276637330…18336171582922311681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.538 × 10⁹⁶(97-digit number)

35380023416553274661…36672343165844623361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.076 × 10⁹⁶(97-digit number)

70760046833106549322…73344686331689246721

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