Block #186,167

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/29/2013, 6:17:34 PM · Difficulty 9.8646 · 6,623,153 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

fb5eca5b657e38d27bf1bc926c86ca893cc497ee4424aec2cafee59c0c9b5f31

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Height

#186,167

Difficulty

9.864561

Transactions

Size

203 B

Version

Bits

09dd53e6

Nonce

32,282

Timestamp

9/29/2013, 6:17:34 PM

Confirmations

6,623,153

Mined by

⛏️ P2SHANvtpRa12yh2D3uGdgT2ggcH58QjsraDJz

Merkle Root

da6b4e9553d2c8826df5cdbddd34dd82dc90752c4f53be6bb3bfef8942a6a98b

Transactions (1)

Coinbaseda6b4e9553d2c8…bfef8942a6a98b

1 in → 1 out10.2600 XPM110 B

ANvtpRa1…QjsraDJz

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.

5.276 × 10¹⁰⁰(101-digit number)

52764780658437907758…20224513973357168641

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

5.276 × 10¹⁰⁰(101-digit number)

52764780658437907758…20224513973357168641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.055 × 10¹⁰¹(102-digit number)

10552956131687581551…40449027946714337281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.110 × 10¹⁰¹(102-digit number)

21105912263375163103…80898055893428674561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.221 × 10¹⁰¹(102-digit number)

42211824526750326207…61796111786857349121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.442 × 10¹⁰¹(102-digit number)

84423649053500652414…23592223573714698241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.688 × 10¹⁰²(103-digit number)

16884729810700130482…47184447147429396481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.376 × 10¹⁰²(103-digit number)

33769459621400260965…94368894294858792961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.753 × 10¹⁰²(103-digit number)

67538919242800521931…88737788589717585921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.350 × 10¹⁰³(104-digit number)

13507783848560104386…77475577179435171841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.701 × 10¹⁰³(104-digit number)

27015567697120208772…54951154358870343681

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 #186,167

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