Block #125,982

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/20/2013, 2:29:00 PM · Difficulty 9.7789 · 6,679,378 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7ccf40c2e7cbbbe39b22c9819cf91918c3910cce3863e88c6239f4adc8b84439

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Height

#125,982

Difficulty

9.778917

Transactions

Size

201 B

Version

Bits

09c7671c

Nonce

284,761

Timestamp

8/20/2013, 2:29:00 PM

Confirmations

6,679,378

Mined by

⛏️ P2SHAN9xPr3qWLtAAMYaTu7JZzCVPkCZEedeL3

Merkle Root

14d75ee7b4e112c8716af222b8b19a8283775097c2fea34c6463666a952f3aba

Transactions (1)

Coinbase14d75ee7b4e112…63666a952f3aba

1 in → 1 out10.4400 XPM109 B

AN9xPr3q…CZEedeL3

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.

1.140 × 10¹⁰⁰(101-digit number)

11408171058656961234…17100655640521510191

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

1.140 × 10¹⁰⁰(101-digit number)

11408171058656961234…17100655640521510191

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.281 × 10¹⁰⁰(101-digit number)

22816342117313922468…34201311281043020381

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.563 × 10¹⁰⁰(101-digit number)

45632684234627844937…68402622562086040761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.126 × 10¹⁰⁰(101-digit number)

91265368469255689875…36805245124172081521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.825 × 10¹⁰¹(102-digit number)

18253073693851137975…73610490248344163041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.650 × 10¹⁰¹(102-digit number)

36506147387702275950…47220980496688326081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.301 × 10¹⁰¹(102-digit number)

73012294775404551900…94441960993376652161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.460 × 10¹⁰²(103-digit number)

14602458955080910380…88883921986753304321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.920 × 10¹⁰²(103-digit number)

29204917910161820760…77767843973506608641

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