Block #421,839

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/27/2014, 8:02:47 AM · Difficulty 10.3758 · 6,396,191 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

fc43640be014c67182d0875459ee9566584d6eeaa2e101321e45ccbaa5871f07

View on Chainz ↗

Height

#421,839

Difficulty

10.375784

Transactions

Size

968 B

Version

Bits

0a60335a

Nonce

86,230

Timestamp

2/27/2014, 8:02:47 AM

Confirmations

6,396,191

Mined by

⛏️ oaSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

9084ac3872cc3eb928449fd114c08f1c25296edc23dcb99c2dda303a4660492b

Transactions (1)

Coinbase9084ac3872cc3e…da303a4660492b

1 in → 24 out9.2700 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH 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.

3.894 × 10⁹²(93-digit number)

38942407746727401849…14298181638669086119

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

3.894 × 10⁹²(93-digit number)

38942407746727401849…14298181638669086119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.788 × 10⁹²(93-digit number)

77884815493454803698…28596363277338172239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.557 × 10⁹³(94-digit number)

15576963098690960739…57192726554676344479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.115 × 10⁹³(94-digit number)

31153926197381921479…14385453109352688959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.230 × 10⁹³(94-digit number)

62307852394763842958…28770906218705377919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.246 × 10⁹⁴(95-digit number)

12461570478952768591…57541812437410755839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.492 × 10⁹⁴(95-digit number)

24923140957905537183…15083624874821511679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.984 × 10⁹⁴(95-digit number)

49846281915811074367…30167249749643023359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.969 × 10⁹⁴(95-digit number)

99692563831622148734…60334499499286046719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.993 × 10⁹⁵(96-digit number)

19938512766324429746…20668998998572093439

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

Block #421,839

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