Block #74,561

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/21/2013, 11:47:08 AM · Difficulty 8.9956 · 6,742,299 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2b178e0e1a489b57d07bcc041f0421d91ba92007271d41d36088bf31f050e787

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Height

#74,561

Difficulty

8.995584

Transactions

Size

203 B

Version

Bits

08fede98

Nonce

343

Timestamp

7/21/2013, 11:47:08 AM

Confirmations

6,742,299

Mined by

⛏️ P2SHAH7Eh9GYMSnm23owcXVdfkeuiPK86X1CDg

Merkle Root

ca0e891c2ba6e28ceee4285b9cdfa97e6b40bbe5a46f46c9b5ac49735c82593c

Transactions (1)

Coinbaseca0e891c2ba6e2…ac49735c82593c

1 in → 1 out12.3400 XPM110 B

AH7Eh9GY…K86X1CDg

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.

1.914 × 10¹⁰²(103-digit number)

19147786396525763411…62292776936480987681

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

1.914 × 10¹⁰²(103-digit number)

19147786396525763411…62292776936480987681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.829 × 10¹⁰²(103-digit number)

38295572793051526823…24585553872961975361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.659 × 10¹⁰²(103-digit number)

76591145586103053647…49171107745923950721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.531 × 10¹⁰³(104-digit number)

15318229117220610729…98342215491847901441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.063 × 10¹⁰³(104-digit number)

30636458234441221459…96684430983695802881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.127 × 10¹⁰³(104-digit number)

61272916468882442918…93368861967391605761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.225 × 10¹⁰⁴(105-digit number)

12254583293776488583…86737723934783211521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.450 × 10¹⁰⁴(105-digit number)

24509166587552977167…73475447869566423041

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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

Block #74,561

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