Block #59,840

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 4:36:18 AM · Difficulty 8.9667 · 6,731,100 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

3c96b91d820856240452d89d5df88d1b5c79c0ca441a9562cc76c3e5c9190779

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Height

#59,840

Difficulty

8.966678

Transactions

Size

1.05 KB

Version

Bits

08f77837

Nonce

Timestamp

7/18/2013, 4:36:18 AM

Confirmations

6,731,100

Merkle Root

ebeb335d3c84040edb68ac1a8491ded2c5f8d27620a4a05acfa7032d0b4fb957

Transactions (2)

Coinbase63d4414ab5cf6d…f0cf87d72d8686

1 in → 1 out12.4300 XPM110 B

ALnRgybZ…E9QHH8Et

5d4fcd68d64b3b…2b853ed81f7476

7 in → 1 out100.0000 XPM875 B

AYxoT5K3…VLfpXK9w

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.

4.947 × 10⁹⁸(99-digit number)

49470906086761126767…68498202499143009511

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

4.947 × 10⁹⁸(99-digit number)

49470906086761126767…68498202499143009511

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

9.894 × 10⁹⁸(99-digit number)

98941812173522253534…36996404998286019021

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.978 × 10⁹⁹(100-digit number)

19788362434704450706…73992809996572038041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.957 × 10⁹⁹(100-digit number)

39576724869408901413…47985619993144076081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.915 × 10⁹⁹(100-digit number)

79153449738817802827…95971239986288152161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.583 × 10¹⁰⁰(101-digit number)

15830689947763560565…91942479972576304321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.166 × 10¹⁰⁰(101-digit number)

31661379895527121131…83884959945152608641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.332 × 10¹⁰⁰(101-digit number)

63322759791054242262…67769919890305217281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.266 × 10¹⁰¹(102-digit number)

12664551958210848452…35539839780610434561

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer