Block #124,040

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/19/2013, 10:02:28 AM · Difficulty 9.7683 · 6,686,935 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

206d800383b7918fdc4f75bd72460ac4bede3e882c93d914b9c250ba268b8055

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Height

#124,040

Difficulty

9.768282

Transactions

Size

202 B

Version

Bits

09c4ae1e

Nonce

373,279

Timestamp

8/19/2013, 10:02:28 AM

Confirmations

6,686,935

Mined by

⛏️ P2SHAcecj4WYP2kTRjXJMUTPed41WTwKtCNbS5

Merkle Root

15767a078b1e5702d352552fbb383226b167d5ad635cd7c503d5ee9daf204866

Transactions (1)

Coinbase15767a078b1e57…d5ee9daf204866

1 in → 1 out10.4600 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.

5.147 × 10¹⁰¹(102-digit number)

51473923185409385753…01355621478311265321

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

5.147 × 10¹⁰¹(102-digit number)

51473923185409385753…01355621478311265321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.029 × 10¹⁰²(103-digit number)

10294784637081877150…02711242956622530641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.058 × 10¹⁰²(103-digit number)

20589569274163754301…05422485913245061281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.117 × 10¹⁰²(103-digit number)

41179138548327508602…10844971826490122561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.235 × 10¹⁰²(103-digit number)

82358277096655017204…21689943652980245121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.647 × 10¹⁰³(104-digit number)

16471655419331003440…43379887305960490241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.294 × 10¹⁰³(104-digit number)

32943310838662006881…86759774611920980481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.588 × 10¹⁰³(104-digit number)

65886621677324013763…73519549223841960961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.317 × 10¹⁰⁴(105-digit number)

13177324335464802752…47039098447683921921

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 #124,040

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