Block #186,226

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/29/2013, 7:12:26 PM · Difficulty 9.8647 · 6,606,469 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

13ca7ea6b998d09889e4a6425389b0707e52ba553a4f0373f5a9f5edf5342ad0

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Height

#186,226

Difficulty

9.864664

Transactions

Size

205 B

Version

Bits

09dd5aa2

Nonce

16,778,060

Timestamp

9/29/2013, 7:12:26 PM

Confirmations

6,606,469

Merkle Root

d14c264d246d5c561a7be20bd7d27358ce6c1386b2b7a4998cb2f129bcd52002

Transactions (1)

Coinbased14c264d246d5c…b2f129bcd52002

1 in → 1 out10.2600 XPM116 B

AcLBm5Z9…S683d7c3

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.

1.411 × 10⁹²(93-digit number)

14115038387934616939…19199745190457753601

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

1.411 × 10⁹²(93-digit number)

14115038387934616939…19199745190457753601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.823 × 10⁹²(93-digit number)

28230076775869233878…38399490380915507201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.646 × 10⁹²(93-digit number)

56460153551738467756…76798980761831014401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.129 × 10⁹³(94-digit number)

11292030710347693551…53597961523662028801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.258 × 10⁹³(94-digit number)

22584061420695387102…07195923047324057601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.516 × 10⁹³(94-digit number)

45168122841390774205…14391846094648115201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.033 × 10⁹³(94-digit number)

90336245682781548410…28783692189296230401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.806 × 10⁹⁴(95-digit number)

18067249136556309682…57567384378592460801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.613 × 10⁹⁴(95-digit number)

36134498273112619364…15134768757184921601

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