Block #379,236

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/28/2014, 10:01:18 AM · Difficulty 10.4153 · 6,425,902 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

55257f7abd334af7157f9f87f7c23e12e02cf903fb76018007b90190cce47598

View on Chainz ↗

Height

#379,236

Difficulty

10.415280

Transactions

Size

35.96 KB

Version

Bits

0a6a4fd2

Nonce

13,805

Timestamp

1/28/2014, 10:01:18 AM

Confirmations

6,425,902

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

53c22da24812e41e798547157df700a344759f27ad192b242933a1f6a66cc3ac

Transactions (2)

Coinbaseab4dc77b2a6f3d…69c2a485e7e274

1 in → 1 out9.5700 XPM116 B

AbwWkWZt…kawDhufa

da1b432c299bb1…d591e05f5cf781

247 in → 2 out500.0100 XPM35.76 KB

Aej9qbTn…k2FbEVKK AJjnK9uC…VreFquR4

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.

3.254 × 10⁹¹(92-digit number)

32546909175452602300…56283162118407937159

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

3.254 × 10⁹¹(92-digit number)

32546909175452602300…56283162118407937159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.509 × 10⁹¹(92-digit number)

65093818350905204600…12566324236815874319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.301 × 10⁹²(93-digit number)

13018763670181040920…25132648473631748639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.603 × 10⁹²(93-digit number)

26037527340362081840…50265296947263497279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.207 × 10⁹²(93-digit number)

52075054680724163680…00530593894526994559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.041 × 10⁹³(94-digit number)

10415010936144832736…01061187789053989119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.083 × 10⁹³(94-digit number)

20830021872289665472…02122375578107978239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.166 × 10⁹³(94-digit number)

41660043744579330944…04244751156215956479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.332 × 10⁹³(94-digit number)

83320087489158661888…08489502312431912959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.666 × 10⁹⁴(95-digit number)

16664017497831732377…16979004624863825919

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