Block #302,357

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/9/2013, 6:43:48 PM · Difficulty 9.9927 · 6,490,159 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ce1f63fbd50fd762ce98cdb5573bfa9d4e59a3010fd8ed944be72d542b64c09a

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Height

#302,357

Difficulty

9.992686

Transactions

Size

1.04 KB

Version

Bits

09fe20a7

Nonce

359,022

Timestamp

12/9/2013, 6:43:48 PM

Confirmations

6,490,159

Merkle Root

00bdd1d8d05c882dc0a2a8192aff9b353c4378bf97b9b98abf39607d8ae5cc78

Transactions (1)

Coinbase00bdd1d8d05c88…39607d8ae5cc78

1 in → 27 out10.0000 XPM981 B

AYtDvcGs…VuAcA7m7 AHuJ9wYh…BGmgHrKZ Ad9pSzHt…cpJ3y2zz Ae6gEbs5…m5Mn8oYw AQyr8Lw3…hs4nt3Pn

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.

1.430 × 10⁹³(94-digit number)

14306068450454898745…02996358404940273441

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

1.430 × 10⁹³(94-digit number)

14306068450454898745…02996358404940273441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.861 × 10⁹³(94-digit number)

28612136900909797491…05992716809880546881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.722 × 10⁹³(94-digit number)

57224273801819594983…11985433619761093761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.144 × 10⁹⁴(95-digit number)

11444854760363918996…23970867239522187521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.288 × 10⁹⁴(95-digit number)

22889709520727837993…47941734479044375041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.577 × 10⁹⁴(95-digit number)

45779419041455675986…95883468958088750081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.155 × 10⁹⁴(95-digit number)

91558838082911351973…91766937916177500161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.831 × 10⁹⁵(96-digit number)

18311767616582270394…83533875832355000321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.662 × 10⁹⁵(96-digit number)

36623535233164540789…67067751664710000641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.324 × 10⁹⁵(96-digit number)

73247070466329081578…34135503329420001281

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