Block #446,547

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/16/2014, 3:49:44 PM · Difficulty 10.3595 · 6,343,523 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

25db14f1842814eaaf5db6241aec6948a466e13b87a83481d4d92534d5362119

View on Chainz ↗

Height

#446,547

Difficulty

10.359516

Transactions

Size

1.20 KB

Version

Bits

0a5c0942

Nonce

569,234

Timestamp

3/16/2014, 3:49:44 PM

Confirmations

6,343,523

Merkle Root

d7f482f9d4ae27427bcf337a35edb7c25eb2d2c33ca0bc040f1afa6ef45fdef2

Transactions (2)

Coinbase890299dcc99eaa…cc1a2cd9952ded

1 in → 1 out9.3200 XPM110 B

AeKNrjNj…1NEq95Ta

b89d4e66e813e4…95edde852a888c

5 in → 11 out30.4753 XPM1.00 KB

AeKNrjNj…1NEq95Ta ASj8XpoA…QL7MgZsp ARpVzkfs…awp11u9T AVrD6maY…W77cdqzz AP4MPyKc…JbZeSack

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.

1.169 × 10⁹⁹(100-digit number)

11694659047164001726…57725221969872724479

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

1.169 × 10⁹⁹(100-digit number)

11694659047164001726…57725221969872724479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.338 × 10⁹⁹(100-digit number)

23389318094328003453…15450443939745448959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.677 × 10⁹⁹(100-digit number)

46778636188656006907…30900887879490897919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.355 × 10⁹⁹(100-digit number)

93557272377312013814…61801775758981795839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.871 × 10¹⁰⁰(101-digit number)

18711454475462402762…23603551517963591679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.742 × 10¹⁰⁰(101-digit number)

37422908950924805525…47207103035927183359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.484 × 10¹⁰⁰(101-digit number)

74845817901849611051…94414206071854366719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.496 × 10¹⁰¹(102-digit number)

14969163580369922210…88828412143708733439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.993 × 10¹⁰¹(102-digit number)

29938327160739844420…77656824287417466879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.987 × 10¹⁰¹(102-digit number)

59876654321479688841…55313648574834933759

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer