Block #72,941

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/21/2013, 3:04:04 AM · Difficulty 8.9945 · 6,738,071 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

7c2fb0cd142680c9a14dcfc70c208f5a8656490cdb66da0906ac2f285aa506fb

View on Chainz ↗

Height

#72,941

Difficulty

8.994457

Transactions

Size

202 B

Version

Bits

08fe94b8

Nonce

Timestamp

7/21/2013, 3:04:04 AM

Confirmations

6,738,071

Mined by

⛏️ P2SHAZDgU5ryLDBgQ43WTK1SQdESypdmcwdqVC

Merkle Root

03472e528517b437de06021c9bf674b1582b68af3cadb74746d8b45e05f23150

Transactions (1)

Coinbase03472e528517b4…d8b45e05f23150

1 in → 1 out12.3400 XPM110 B

AZDgU5ry…dmcwdqVC

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.

1.039 × 10⁹⁹(100-digit number)

10397009298260390314…55209914694108096959

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

1.039 × 10⁹⁹(100-digit number)

10397009298260390314…55209914694108096959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.079 × 10⁹⁹(100-digit number)

20794018596520780628…10419829388216193919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.158 × 10⁹⁹(100-digit number)

41588037193041561257…20839658776432387839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.317 × 10⁹⁹(100-digit number)

83176074386083122515…41679317552864775679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.663 × 10¹⁰⁰(101-digit number)

16635214877216624503…83358635105729551359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.327 × 10¹⁰⁰(101-digit number)

33270429754433249006…66717270211459102719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.654 × 10¹⁰⁰(101-digit number)

66540859508866498012…33434540422918205439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.330 × 10¹⁰¹(102-digit number)

13308171901773299602…66869080845836410879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.661 × 10¹⁰¹(102-digit number)

26616343803546599205…33738161691672821759

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 #72,941

Cookie Preferences