Block #448,658

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/18/2014, 2:22:21 AM · Difficulty 10.3652 · 6,347,172 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

eb6c135d4a5809f1ec4e21c637702dac58d7befb2a0cfb8f4534b74cdb82dcec

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Height

#448,658

Difficulty

10.365247

Transactions

Size

1.05 KB

Version

Bits

0a5d80d0

Nonce

3,920

Timestamp

3/18/2014, 2:22:21 AM

Confirmations

6,347,172

Mined by

⛏️ aS'AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

cb1e430c16ab7552eb7ac66035a2cb424870e323aaad8b4b9bccec1990ba40e0

Transactions (1)

Coinbasecb1e430c16ab75…ccec1990ba40e0

1 in → 27 out9.2900 XPM981 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 AWMrD5hP…ZwsoxvZ3

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.

9.204 × 10⁹⁸(99-digit number)

92045213018371019718…52999977619928108801

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

9.204 × 10⁹⁸(99-digit number)

92045213018371019718…52999977619928108801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.840 × 10⁹⁹(100-digit number)

18409042603674203943…05999955239856217601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.681 × 10⁹⁹(100-digit number)

36818085207348407887…11999910479712435201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.363 × 10⁹⁹(100-digit number)

73636170414696815774…23999820959424870401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.472 × 10¹⁰⁰(101-digit number)

14727234082939363154…47999641918849740801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.945 × 10¹⁰⁰(101-digit number)

29454468165878726309…95999283837699481601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.890 × 10¹⁰⁰(101-digit number)

58908936331757452619…91998567675398963201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.178 × 10¹⁰¹(102-digit number)

11781787266351490523…83997135350797926401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.356 × 10¹⁰¹(102-digit number)

23563574532702981047…67994270701595852801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.712 × 10¹⁰¹(102-digit number)

47127149065405962095…35988541403191705601

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