Block #95,634

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/3/2013, 7:28:27 PM · Difficulty 9.2319 · 6,734,860 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c8d50394cae37948783cc0442304a15372562220bc5b931ce178b71ccd8a69a8

View on Chainz ↗

Height

#95,634

Difficulty

9.231883

Transactions

Size

205 B

Version

Bits

093b5cae

Nonce

35,320

Timestamp

8/3/2013, 7:28:27 PM

Confirmations

6,734,860

Mined by

⛏️ P2SHASBXxde64Zv3d4wbyCawpFpHVzHx9z9eQS

Merkle Root

243ca057a3cf84698c5e4011a67aadf15622947f204823ea1f9a19bfa12558c1

Transactions (1)

Coinbase243ca057a3cf84…9a19bfa12558c1

1 in → 1 out11.7200 XPM109 B

ASBXxde6…Hx9z9eQS

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.

5.896 × 10¹⁰⁸(109-digit number)

58968357180387222713…17564093333515930601

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

5.896 × 10¹⁰⁸(109-digit number)

58968357180387222713…17564093333515930601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.179 × 10¹⁰⁹(110-digit number)

11793671436077444542…35128186667031861201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.358 × 10¹⁰⁹(110-digit number)

23587342872154889085…70256373334063722401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.717 × 10¹⁰⁹(110-digit number)

47174685744309778170…40512746668127444801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.434 × 10¹⁰⁹(110-digit number)

94349371488619556341…81025493336254889601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.886 × 10¹¹⁰(111-digit number)

18869874297723911268…62050986672509779201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.773 × 10¹¹⁰(111-digit number)

37739748595447822536…24101973345019558401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.547 × 10¹¹⁰(111-digit number)

75479497190895645073…48203946690039116801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.509 × 10¹¹¹(112-digit number)

15095899438179129014…96407893380078233601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.019 × 10¹¹¹(112-digit number)

30191798876358258029…92815786760156467201

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #95,634

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