Block #277,245

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/27/2013, 12:12:17 PM · Difficulty 9.9657 · 6,532,802 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b14df1bdab72d5725c720213c5a4894f90badb03c934c804dcc6eafd065a048c

View on Chainz ↗

Height

#277,245

Difficulty

9.965667

Transactions

Size

1.12 KB

Version

Bits

09f735fa

Nonce

949

Timestamp

11/27/2013, 12:12:17 PM

Confirmations

6,532,802

Mined by

⛏️ :aRsAWGQhzDNqt1A9FGXDdvgYQjDXoRDYvugUy

Merkle Root

1144b2b9a960b54f259b3e40af7a6887aafc284b6f966a5cf6d55fb42411be9e

Transactions (1)

Coinbase1144b2b9a960b5…d55fb42411be9e

1 in → 29 out10.0300 XPM1.02 KB

AWGQhzDN…RDYvugUy AScAzqGc…BZ6tV1vJ Abv8pzf1…t4zPXDTV AN8nUzff…YcDfRDQ2 AbiApRgN…g8QuFUwL

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.

6.192 × 10¹⁰⁶(107-digit number)

61922734230260552637…92818833247803730239

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

6.192 × 10¹⁰⁶(107-digit number)

61922734230260552637…92818833247803730239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.238 × 10¹⁰⁷(108-digit number)

12384546846052110527…85637666495607460479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.476 × 10¹⁰⁷(108-digit number)

24769093692104221054…71275332991214920959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.953 × 10¹⁰⁷(108-digit number)

49538187384208442109…42550665982429841919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.907 × 10¹⁰⁷(108-digit number)

99076374768416884219…85101331964859683839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.981 × 10¹⁰⁸(109-digit number)

19815274953683376843…70202663929719367679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.963 × 10¹⁰⁸(109-digit number)

39630549907366753687…40405327859438735359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.926 × 10¹⁰⁸(109-digit number)

79261099814733507375…80810655718877470719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.585 × 10¹⁰⁹(110-digit number)

15852219962946701475…61621311437754941439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #277,245

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