Block #383,344

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/31/2014, 8:47:40 AM · Difficulty 10.4004 · 6,420,187 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e418501a6f86797f6795d167fc42160f283136a8f07916250d4a97bcb9007512

View on Chainz ↗

Height

#383,344

Difficulty

10.400365

Transactions

Size

399 B

Version

Bits

0a667e54

Nonce

2,608

Timestamp

1/31/2014, 8:47:40 AM

Confirmations

6,420,187

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

7027af8774a992b368557e8c69a04267e071c4eb15a27652eed0494e02cc3d3f

Transactions (2)

Coinbase2534a105f234db…a415ec08440023

1 in → 1 out9.2400 XPM116 B

AbwWkWZt…kawDhufa

50686e28ab5049…77f518e3430fca

1 in → 1 out2.9909 XPM193 B

AKphT6Ys…qYJza4Du

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.

3.588 × 10⁹⁴(95-digit number)

35884780427654048100…80703957416654425601

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

3.588 × 10⁹⁴(95-digit number)

35884780427654048100…80703957416654425601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.176 × 10⁹⁴(95-digit number)

71769560855308096200…61407914833308851201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.435 × 10⁹⁵(96-digit number)

14353912171061619240…22815829666617702401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.870 × 10⁹⁵(96-digit number)

28707824342123238480…45631659333235404801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.741 × 10⁹⁵(96-digit number)

57415648684246476960…91263318666470809601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.148 × 10⁹⁶(97-digit number)

11483129736849295392…82526637332941619201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.296 × 10⁹⁶(97-digit number)

22966259473698590784…65053274665883238401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.593 × 10⁹⁶(97-digit number)

45932518947397181568…30106549331766476801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

9.186 × 10⁹⁶(97-digit number)

91865037894794363136…60213098663532953601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.837 × 10⁹⁷(98-digit number)

18373007578958872627…20426197327065907201

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