Block #268,926

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/22/2013, 2:05:51 PM · Difficulty 9.9559 · 6,525,215 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e0f31dc3a1e78629cb38d7ce3191b6098c186146af4ad6d11f97770392028177

View on Chainz ↗

Height

#268,926

Difficulty

9.955851

Transactions

Size

562 B

Version

Bits

09f4b2af

Nonce

1,569

Timestamp

11/22/2013, 2:05:51 PM

Confirmations

6,525,215

Merkle Root

ae54c8deb263ac868d74a4e03aaf72e271f00cf03c2fc0ed08b3a7421de3e4a2

Transactions (2)

Coinbase9da2c7c03943ad…d9e1cfd2d825af

1 in → 1 out10.0800 XPM100 B

AbGkvdxH…oihMdBXd

4efe0dd632000a…e299c179aab79e

2 in → 2 out128.4054 XPM373 B

AcaLnXPa…dituQhDU AX65w2u1…U9FMmnRi

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.

2.664 × 10⁹³(94-digit number)

26641970796609650439…46748078551302990841

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

2.664 × 10⁹³(94-digit number)

26641970796609650439…46748078551302990841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.328 × 10⁹³(94-digit number)

53283941593219300879…93496157102605981681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.065 × 10⁹⁴(95-digit number)

10656788318643860175…86992314205211963361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.131 × 10⁹⁴(95-digit number)

21313576637287720351…73984628410423926721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.262 × 10⁹⁴(95-digit number)

42627153274575440703…47969256820847853441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.525 × 10⁹⁴(95-digit number)

85254306549150881407…95938513641695706881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.705 × 10⁹⁵(96-digit number)

17050861309830176281…91877027283391413761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.410 × 10⁹⁵(96-digit number)

34101722619660352562…83754054566782827521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.820 × 10⁹⁵(96-digit number)

68203445239320705125…67508109133565655041

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