Block #428,405

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/4/2014, 1:36:27 AM · Difficulty 10.3473 · 6,377,502 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

c02d881b9f84dfca14b48ea2753b09d575f132a726016b31868579db48d5290b

View on Chainz ↗

Height

#428,405

Difficulty

10.347349

Transactions

Size

836 B

Version

Bits

0a58ebd6

Nonce

128,751

Timestamp

3/4/2014, 1:36:27 AM

Confirmations

6,377,502

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

12862c4ef1ed7a560ad2a96382f4ae28765cb204d79c436d31385517f6b9b960

Transactions (2)

Coinbased995d60e743d27…f16671469df88b

1 in → 1 out9.3400 XPM110 B

AeKNrjNj…1NEq95Ta

8fce9b7b76673b…469ecf541fc879

4 in → 1 out999.9900 XPM637 B

AKrKmUfb…jUQpKaoH

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.

1.648 × 10⁹³(94-digit number)

16485334229857605405…52041036547367024119

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

1.648 × 10⁹³(94-digit number)

16485334229857605405…52041036547367024119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.297 × 10⁹³(94-digit number)

32970668459715210811…04082073094734048239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.594 × 10⁹³(94-digit number)

65941336919430421623…08164146189468096479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.318 × 10⁹⁴(95-digit number)

13188267383886084324…16328292378936192959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.637 × 10⁹⁴(95-digit number)

26376534767772168649…32656584757872385919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.275 × 10⁹⁴(95-digit number)

52753069535544337298…65313169515744771839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.055 × 10⁹⁵(96-digit number)

10550613907108867459…30626339031489543679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.110 × 10⁹⁵(96-digit number)

21101227814217734919…61252678062979087359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.220 × 10⁹⁵(96-digit number)

42202455628435469839…22505356125958174719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.440 × 10⁹⁵(96-digit number)

84404911256870939678…45010712251916349439

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