Block #135,561

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/26/2013, 5:02:49 PM · Difficulty 9.8111 · 6,678,748 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

82d855a84e9a966d21feba04f9d6a9175c7bd5b7193ef963d2d6e29d9cb969b0

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Height

#135,561

Difficulty

9.811121

Transactions

Size

4.21 KB

Version

Bits

09cfa5a6

Nonce

25,045

Timestamp

8/26/2013, 5:02:49 PM

Confirmations

6,678,748

Mined by

⛏️ P2SHAFxtmUWznEiuhXKxrBKXNPp6oCsND4q5cA

Merkle Root

b7e64c8253a99a8a6452d5aa9386708f441e84db13e3d3aa0db1465737fb1d92

Transactions (2)

Coinbase47045d527a950b…c68ea13defb59c

1 in → 1 out10.4200 XPM109 B

AFxtmUWz…sND4q5cA

ae1d2b7b9d5a1d…41bd1cad7d5238

33 in → 2 out400.0107 XPM4.02 KB

AbMEW2LJ…Ntb1rfN5 AM6vjhTo…f7Nt8tSJ

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.

3.304 × 10⁸⁸(89-digit number)

33047604683679339709…22424126340565779001

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

3.304 × 10⁸⁸(89-digit number)

33047604683679339709…22424126340565779001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.609 × 10⁸⁸(89-digit number)

66095209367358679418…44848252681131558001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.321 × 10⁸⁹(90-digit number)

13219041873471735883…89696505362263116001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.643 × 10⁸⁹(90-digit number)

26438083746943471767…79393010724526232001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.287 × 10⁸⁹(90-digit number)

52876167493886943534…58786021449052464001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.057 × 10⁹⁰(91-digit number)

10575233498777388706…17572042898104928001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.115 × 10⁹⁰(91-digit number)

21150466997554777413…35144085796209856001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.230 × 10⁹⁰(91-digit number)

42300933995109554827…70288171592419712001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.460 × 10⁹⁰(91-digit number)

84601867990219109655…40576343184839424001

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

Block #135,561

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