Block #288,927

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/1/2013, 11:39:06 PM · Difficulty 9.9881 · 6,505,213 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

bbb0834aaa5f2478b4ae0fa11ac87ec9424ffd292d31c62b728d7bdeef0abe44

View on Chainz ↗

Height

#288,927

Difficulty

9.988085

Transactions

Size

1.14 KB

Version

Bits

09fcf31c

Nonce

130,593

Timestamp

12/1/2013, 11:39:06 PM

Confirmations

6,505,213

Merkle Root

5c674074e477316f6c5c48f0333597babd26012b4ccbd4669c5090ae17a37289

Transactions (1)

Coinbase5c674074e47731…5090ae17a37289

1 in → 30 out9.9900 XPM1.06 KB

ASXEwJrb…E3MLWChF ANt4qZJR…v3reHqRo AWZd1qVJ…9pj9yfPa AHqZtsfn…WrCGjM3J AKxUhrcX…56oFrcLK

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.

1.421 × 10⁹³(94-digit number)

14216176162071115628…99166508076115978741

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

1.421 × 10⁹³(94-digit number)

14216176162071115628…99166508076115978741

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.843 × 10⁹³(94-digit number)

28432352324142231257…98333016152231957481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.686 × 10⁹³(94-digit number)

56864704648284462515…96666032304463914961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.137 × 10⁹⁴(95-digit number)

11372940929656892503…93332064608927829921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.274 × 10⁹⁴(95-digit number)

22745881859313785006…86664129217855659841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.549 × 10⁹⁴(95-digit number)

45491763718627570012…73328258435711319681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.098 × 10⁹⁴(95-digit number)

90983527437255140025…46656516871422639361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.819 × 10⁹⁵(96-digit number)

18196705487451028005…93313033742845278721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.639 × 10⁹⁵(96-digit number)

36393410974902056010…86626067485690557441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.278 × 10⁹⁵(96-digit number)

72786821949804112020…73252134971381114881

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