Block #125,597

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/20/2013, 8:49:44 AM · Difficulty 9.7769 · 6,679,548 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

5cffe5bb1e1e7e87d1a2b7e492556a58abb1f5afa7afe30e1a635cb48c031063

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Height

#125,597

Difficulty

9.776881

Transactions

Size

201 B

Version

Bits

09c6e1a7

Nonce

180,414

Timestamp

8/20/2013, 8:49:44 AM

Confirmations

6,679,548

Mined by

⛏️ P2SHAcecj4WYP2kTRjXJMUTPed41WTwKtCNbS5

Merkle Root

ef768315d40246fd72df966b3a56e45b2f33659dd16a6fa5b0f27f06cbf2b16d

Transactions (1)

Coinbaseef768315d40246…f27f06cbf2b16d

1 in → 1 out10.4500 XPM109 B

Acecj4WY…wKtCNbS5

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.

2.533 × 10¹⁰⁰(101-digit number)

25338155221052161539…49346317574368896961

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

2.533 × 10¹⁰⁰(101-digit number)

25338155221052161539…49346317574368896961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.067 × 10¹⁰⁰(101-digit number)

50676310442104323079…98692635148737793921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.013 × 10¹⁰¹(102-digit number)

10135262088420864615…97385270297475587841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.027 × 10¹⁰¹(102-digit number)

20270524176841729231…94770540594951175681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.054 × 10¹⁰¹(102-digit number)

40541048353683458463…89541081189902351361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.108 × 10¹⁰¹(102-digit number)

81082096707366916927…79082162379804702721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.621 × 10¹⁰²(103-digit number)

16216419341473383385…58164324759609405441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.243 × 10¹⁰²(103-digit number)

32432838682946766771…16328649519218810881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.486 × 10¹⁰²(103-digit number)

64865677365893533542…32657299038437621761

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