Block #288,767

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/1/2013, 10:05:13 PM · Difficulty 9.9879 · 6,513,823 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d497e5700a0247d2970455e2ca0bf4f4ef295c5b2f398849f3f12d467f5b2009

View on Chainz ↗

Height

#288,767

Difficulty

9.987925

Transactions

Size

1.14 KB

Version

Bits

09fce8af

Nonce

103,230

Timestamp

12/1/2013, 10:05:13 PM

Confirmations

6,513,823

Mined by

⛏️ gaRfAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

326d592644b137f7f912f59dc16c53c43df2ff59dad3cea9c85ef26ad5d1d9bd

Transactions (1)

Coinbase326d592644b137…5ef26ad5d1d9bd

1 in → 30 out9.9900 XPM1.06 KB

Ad9pSzHt…cpJ3y2zz AYcLTeXR…bscgPops AKEwr54i…9BfmMkRh AGFAJ5YL…ZEnBbk6G ASXEwJrb…E3MLWChF

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.

3.027 × 10⁸⁸(89-digit number)

30276733969686006375…36090230843534248001

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

3.027 × 10⁸⁸(89-digit number)

30276733969686006375…36090230843534248001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.055 × 10⁸⁸(89-digit number)

60553467939372012751…72180461687068496001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.211 × 10⁸⁹(90-digit number)

12110693587874402550…44360923374136992001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.422 × 10⁸⁹(90-digit number)

24221387175748805100…88721846748273984001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.844 × 10⁸⁹(90-digit number)

48442774351497610201…77443693496547968001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.688 × 10⁸⁹(90-digit number)

96885548702995220402…54887386993095936001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.937 × 10⁹⁰(91-digit number)

19377109740599044080…09774773986191872001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.875 × 10⁹⁰(91-digit number)

38754219481198088161…19549547972383744001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.750 × 10⁹⁰(91-digit number)

77508438962396176322…39099095944767488001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.550 × 10⁹¹(92-digit number)

15501687792479235264…78198191889534976001

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