Block #432,651

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/7/2014, 1:45:21 AM · Difficulty 10.3410 · 6,370,627 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

7b596f901728ba3e8e1a89891cf982d0d012743fefd9564179ffb99964269ca4

View on Chainz ↗

Height

#432,651

Difficulty

10.340980

Transactions

Size

22.53 KB

Version

Bits

0a574a77

Nonce

25,506

Timestamp

3/7/2014, 1:45:21 AM

Confirmations

6,370,627

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

7985ab9b1081f08a38d618689ec2860c9e1ba38644feb772d5e97b68053ddb2e

Transactions (2)

Coinbase66ca86914aba10…fd0ea212fabf29

1 in → 1 out9.5800 XPM110 B

AeKNrjNj…1NEq95Ta

3228a1ceaaa83b…6cb1ccbc40dac0

158 in → 2 out201.0545 XPM22.33 KB

AXTPneii…aJqW2NBa AR24vtgA…DNdtqa6z

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.

1.649 × 10⁹⁷(98-digit number)

16493474346016855106…74007814608855111679

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

1.649 × 10⁹⁷(98-digit number)

16493474346016855106…74007814608855111679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.298 × 10⁹⁷(98-digit number)

32986948692033710212…48015629217710223359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.597 × 10⁹⁷(98-digit number)

65973897384067420424…96031258435420446719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.319 × 10⁹⁸(99-digit number)

13194779476813484084…92062516870840893439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.638 × 10⁹⁸(99-digit number)

26389558953626968169…84125033741681786879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.277 × 10⁹⁸(99-digit number)

52779117907253936339…68250067483363573759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.055 × 10⁹⁹(100-digit number)

10555823581450787267…36500134966727147519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.111 × 10⁹⁹(100-digit number)

21111647162901574535…73000269933454295039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.222 × 10⁹⁹(100-digit number)

42223294325803149071…46000539866908590079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.444 × 10⁹⁹(100-digit number)

84446588651606298143…92001079733817180159

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