Block #447,316

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/17/2014, 5:17:48 AM · Difficulty 10.3541 · 6,353,416 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

6b484acc7ae28bf8a83b2f377a99c7a7208c62acb97e696e4ae3eeefb70c91ef

View on Chainz ↗

Height

#447,316

Difficulty

10.354129

Transactions

Size

1004 B

Version

Bits

0a5aa835

Nonce

38,308

Timestamp

3/17/2014, 5:17:48 AM

Confirmations

6,353,416

Mined by

⛏️ TaS&dAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

439a7a9d1607d1663a390a2128ad2b081a93c6886aef9910f773de7acdd07d6f

Transactions (1)

Coinbase439a7a9d1607d1…73de7acdd07d6f

1 in → 25 out9.3100 XPM913 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

1.677 × 10⁹⁶(97-digit number)

16774959222652786413…16535229132887256001

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

1.677 × 10⁹⁶(97-digit number)

16774959222652786413…16535229132887256001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.354 × 10⁹⁶(97-digit number)

33549918445305572827…33070458265774512001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.709 × 10⁹⁶(97-digit number)

67099836890611145655…66140916531549024001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.341 × 10⁹⁷(98-digit number)

13419967378122229131…32281833063098048001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.683 × 10⁹⁷(98-digit number)

26839934756244458262…64563666126196096001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.367 × 10⁹⁷(98-digit number)

53679869512488916524…29127332252392192001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.073 × 10⁹⁸(99-digit number)

10735973902497783304…58254664504784384001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.147 × 10⁹⁸(99-digit number)

21471947804995566609…16509329009568768001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.294 × 10⁹⁸(99-digit number)

42943895609991133219…33018658019137536001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

8.588 × 10⁹⁸(99-digit number)

85887791219982266438…66037316038275072001

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