Block #249,556

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/8/2013, 12:52:06 AM · Difficulty 9.9670 · 6,557,115 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

03ef19bfb45bc014a7e27a7e01140940eedac37d04783d3d707028d3c6501309

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Height

#249,556

Difficulty

9.967034

Transactions

Size

2.54 KB

Version

Bits

09f78f8b

Nonce

94,238

Timestamp

11/8/2013, 12:52:06 AM

Confirmations

6,557,115

Mined by

⛏️ R|5AGbRhLj1HQi4pXYvW1G5HRrmefnZcEQFqQ

Merkle Root

a52b21d9c9cb2a34bb5e6b3071ae644d1b132034deccab0be46d81125142dcd2

Transactions (1)

Coinbasea52b21d9c9cb2a…6d81125142dcd2

1 in → 72 out10.0200 XPM2.45 KB

AGbRhLj1…nZcEQFqQ ANuKx9Ke…wm7nrBRq AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY AHkgKuuD…TkWqWiw1

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.

2.324 × 10⁸⁸(89-digit number)

23245506353819374302…88339082634561527601

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

2.324 × 10⁸⁸(89-digit number)

23245506353819374302…88339082634561527601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.649 × 10⁸⁸(89-digit number)

46491012707638748604…76678165269123055201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.298 × 10⁸⁸(89-digit number)

92982025415277497208…53356330538246110401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.859 × 10⁸⁹(90-digit number)

18596405083055499441…06712661076492220801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.719 × 10⁸⁹(90-digit number)

37192810166110998883…13425322152984441601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.438 × 10⁸⁹(90-digit number)

74385620332221997766…26850644305968883201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.487 × 10⁹⁰(91-digit number)

14877124066444399553…53701288611937766401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.975 × 10⁹⁰(91-digit number)

29754248132888799106…07402577223875532801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.950 × 10⁹⁰(91-digit number)

59508496265777598213…14805154447751065601

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 #249,556

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