Block #97,372

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/4/2013, 4:36:09 PM · Difficulty 9.3039 · 6,707,423 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c6f30f6468c2a45baa235151304d473cced3633378befc9229e45eaa6634f37c

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Height

#97,372

Difficulty

9.303856

Transactions

Size

200 B

Version

Bits

094dc981

Nonce

1,046,543

Timestamp

8/4/2013, 4:36:09 PM

Confirmations

6,707,423

Mined by

⛏️ P2SHAMdSjDTRZ6cZHDeywQmh2ASnDLUXEoSyLN

Merkle Root

201c7cc94629c00d5c984e02bfdda1db421d88f50af9881d7d35bd9665d4470d

Transactions (1)

Coinbase201c7cc94629c0…35bd9665d4470d

1 in → 1 out11.5400 XPM109 B

AMdSjDTR…UXEoSyLN

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.

1.208 × 10⁹⁸(99-digit number)

12089122000850383773…06378104433175578791

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

1.208 × 10⁹⁸(99-digit number)

12089122000850383773…06378104433175578791

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.417 × 10⁹⁸(99-digit number)

24178244001700767547…12756208866351157581

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.835 × 10⁹⁸(99-digit number)

48356488003401535094…25512417732702315161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.671 × 10⁹⁸(99-digit number)

96712976006803070189…51024835465404630321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.934 × 10⁹⁹(100-digit number)

19342595201360614037…02049670930809260641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.868 × 10⁹⁹(100-digit number)

38685190402721228075…04099341861618521281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.737 × 10⁹⁹(100-digit number)

77370380805442456151…08198683723237042561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.547 × 10¹⁰⁰(101-digit number)

15474076161088491230…16397367446474085121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.094 × 10¹⁰⁰(101-digit number)

30948152322176982460…32794734892948170241

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