Block #432,619

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/7/2014, 12:51:47 AM · Difficulty 10.3417 · 6,362,401 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ca4838aa81cae94b05449aef0020fc983a7f9637837af175109b9664584d5a74

View on Chainz ↗

Height

#432,619

Difficulty

10.341664

Transactions

Size

902 B

Version

Bits

0a57774b

Nonce

82,919

Timestamp

3/7/2014, 12:51:47 AM

Confirmations

6,362,401

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

750af254b9b995f34f4fd3da40076d2dae10bf37b412b0a02d02b742dcb59902

Transactions (1)

Coinbase750af254b9b995…02b742dcb59902

1 in → 22 out9.3400 XPM811 B

AdFLJFhb…bsaVkAyh AVRMvm7T…6PC6keBx AcuM7XiJ…5uND8Jce AQFhQpUS…HmKbSyAx AZqjMFvv…G8aw2zC8

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.

1.284 × 10⁹⁸(99-digit number)

12845397642067039986…06941006885046717439

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

1.284 × 10⁹⁸(99-digit number)

12845397642067039986…06941006885046717439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.569 × 10⁹⁸(99-digit number)

25690795284134079972…13882013770093434879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.138 × 10⁹⁸(99-digit number)

51381590568268159945…27764027540186869759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.027 × 10⁹⁹(100-digit number)

10276318113653631989…55528055080373739519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.055 × 10⁹⁹(100-digit number)

20552636227307263978…11056110160747479039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.110 × 10⁹⁹(100-digit number)

41105272454614527956…22112220321494958079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.221 × 10⁹⁹(100-digit number)

82210544909229055912…44224440642989916159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.644 × 10¹⁰⁰(101-digit number)

16442108981845811182…88448881285979832319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.288 × 10¹⁰⁰(101-digit number)

32884217963691622365…76897762571959664639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.576 × 10¹⁰⁰(101-digit number)

65768435927383244730…53795525143919329279

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