Block #265,834

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/19/2013, 10:42:51 PM · Difficulty 9.9615 · 6,531,055 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

71d74d569b8a5eeb16ccad6876ca66cbda5eb13abf0037f72a5fec69478493c0

View on Chainz ↗

Height

#265,834

Difficulty

9.961545

Transactions

Size

1.68 KB

Version

Bits

09f627d7

Nonce

121,276

Timestamp

11/19/2013, 10:42:51 PM

Confirmations

6,531,055

Mined by

⛏️ jaRa+AMttQDuftdpMyrb199TXiUSH5L7j6tfS9x

Merkle Root

cf3ad423e9563f8c4b2df7c4db019ae118e37b88bb3ca3776700abce6139f420

Transactions (1)

Coinbasecf3ad423e9563f…00abce6139f420

1 in → 46 out10.0325 XPM1.59 KB

AMttQDuf…7j6tfS9x AKXeSXzu…yeuNjvhB AVzhvfTX…ZzNJYq61 Ac5sZcdP…kzV4eckG AU9KdB9r…o5XC6WMy

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.

5.265 × 10⁹³(94-digit number)

52659806371930575350…75129711136189895021

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

5.265 × 10⁹³(94-digit number)

52659806371930575350…75129711136189895021

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.053 × 10⁹⁴(95-digit number)

10531961274386115070…50259422272379790041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.106 × 10⁹⁴(95-digit number)

21063922548772230140…00518844544759580081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.212 × 10⁹⁴(95-digit number)

42127845097544460280…01037689089519160161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.425 × 10⁹⁴(95-digit number)

84255690195088920561…02075378179038320321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.685 × 10⁹⁵(96-digit number)

16851138039017784112…04150756358076640641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.370 × 10⁹⁵(96-digit number)

33702276078035568224…08301512716153281281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.740 × 10⁹⁵(96-digit number)

67404552156071136448…16603025432306562561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.348 × 10⁹⁶(97-digit number)

13480910431214227289…33206050864613125121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.696 × 10⁹⁶(97-digit number)

26961820862428454579…66412101729226250241

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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