Block #69,730

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/20/2013, 10:11:47 AM · Difficulty 8.9913 · 6,739,025 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c188e1f58d717ad0631f14fa0682b377c41d7934efdfe64bb144e25942d64f3b

View on Chainz ↗

Height

#69,730

Difficulty

8.991304

Transactions

Size

362 B

Version

Bits

08fdc621

Nonce

376

Timestamp

7/20/2013, 10:11:47 AM

Confirmations

6,739,025

Mined by

⛏️ P2SHAd14qRTNDVQvCA7rkyLCNnxYLQQSuX88Fw

Merkle Root

fefd4665d81c1984fa20a377b77c017e4aae22ea026ad432db8fa9018003ebaf

Transactions (2)

Coinbase6b1be26fad9213…2170f0b2e1e82d

1 in → 1 out12.3600 XPM110 B

Ad14qRTN…QSuX88Fw

ba88ba2235e7a5…98c67b8d45b980

1 in → 1 out12.3600 XPM157 B

APNQYaGC…odxqm1da

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.

1.230 × 10¹⁰⁷(108-digit number)

12308523808363176387…00723492610361203001

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

1.230 × 10¹⁰⁷(108-digit number)

12308523808363176387…00723492610361203001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.461 × 10¹⁰⁷(108-digit number)

24617047616726352774…01446985220722406001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.923 × 10¹⁰⁷(108-digit number)

49234095233452705549…02893970441444812001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.846 × 10¹⁰⁷(108-digit number)

98468190466905411098…05787940882889624001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.969 × 10¹⁰⁸(109-digit number)

19693638093381082219…11575881765779248001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.938 × 10¹⁰⁸(109-digit number)

39387276186762164439…23151763531558496001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.877 × 10¹⁰⁸(109-digit number)

78774552373524328878…46303527063116992001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.575 × 10¹⁰⁹(110-digit number)

15754910474704865775…92607054126233984001

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 #69,730

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