Block #255,166

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/11/2013, 3:17:08 AM · Difficulty 9.9739 · 6,560,769 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e7fe06f183d10e1eb4243d0ef3e5ebe54bb546db6064a1a8ac8589e5c6f31327

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Height

#255,166

Difficulty

9.973893

Transactions

Size

1.74 KB

Version

Bits

09f95114

Nonce

52,407

Timestamp

11/11/2013, 3:17:08 AM

Confirmations

6,560,769

Mined by

⛏️ aRLARskhKebzwhUsQms8dTj78qtmaUgDvvX9P

Merkle Root

922e10567af198bc7ea9dff25ab1402e48835ae9e9b582a50032b14e746cc627

Transactions (1)

Coinbase922e10567af198…32b14e746cc627

1 in → 48 out10.0200 XPM1.66 KB

ARskhKeb…UgDvvX9P AdC9so3F…oBavUrdS AQtzUSwq…htAuF3yC AMttQDuf…7j6tfS9x ARR7aRH6…ne3DXGXZ

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.

1.838 × 10⁹⁶(97-digit number)

18384397235361813807…99762436896899896801

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

1.838 × 10⁹⁶(97-digit number)

18384397235361813807…99762436896899896801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.676 × 10⁹⁶(97-digit number)

36768794470723627615…99524873793799793601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.353 × 10⁹⁶(97-digit number)

73537588941447255231…99049747587599587201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.470 × 10⁹⁷(98-digit number)

14707517788289451046…98099495175199174401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.941 × 10⁹⁷(98-digit number)

29415035576578902092…96198990350398348801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.883 × 10⁹⁷(98-digit number)

58830071153157804184…92397980700796697601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.176 × 10⁹⁸(99-digit number)

11766014230631560836…84795961401593395201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.353 × 10⁹⁸(99-digit number)

23532028461263121673…69591922803186790401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.706 × 10⁹⁸(99-digit number)

47064056922526243347…39183845606373580801

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 #255,166

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