Block #304,730

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/11/2013, 2:19:38 AM · Difficulty 9.9934 · 6,500,086 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

461e03de947258f79610815195331918a532e1bf1404335530faf6a557e46019

View on Chainz ↗

Height

#304,730

Difficulty

9.993415

Transactions

Size

1.18 KB

Version

Bits

09fe506f

Nonce

185,975

Timestamp

12/11/2013, 2:19:38 AM

Confirmations

6,500,086

Mined by

⛏️ ZaRAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

959c2ec9e61f7c5f917a06fe7df6d3d57d2e8641bd6ad102990785d1c7b18f7f

Transactions (1)

Coinbase959c2ec9e61f7c…0785d1c7b18f7f

1 in → 31 out9.9800 XPM1.09 KB

Ad9pSzHt…cpJ3y2zz AG5YAjec…VhA4Aeh1 AWjMy3MQ…6SDvk22A AcVAEuoP…1jK61Unr AW4asrzQ…pN7SGYKR

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.

1.583 × 10⁹²(93-digit number)

15834836348033961825…53546841949699732401

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

1.583 × 10⁹²(93-digit number)

15834836348033961825…53546841949699732401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.166 × 10⁹²(93-digit number)

31669672696067923651…07093683899399464801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.333 × 10⁹²(93-digit number)

63339345392135847303…14187367798798929601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.266 × 10⁹³(94-digit number)

12667869078427169460…28374735597597859201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.533 × 10⁹³(94-digit number)

25335738156854338921…56749471195195718401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.067 × 10⁹³(94-digit number)

50671476313708677843…13498942390391436801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.013 × 10⁹⁴(95-digit number)

10134295262741735568…26997884780782873601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.026 × 10⁹⁴(95-digit number)

20268590525483471137…53995769561565747201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.053 × 10⁹⁴(95-digit number)

40537181050966942274…07991539123131494401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

8.107 × 10⁹⁴(95-digit number)

81074362101933884548…15983078246262988801

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