Block #403,166

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/13/2014, 11:31:04 PM · Difficulty 10.4329 · 6,407,937 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c879ef9a76522329bf43dced53c6d7ac573301b6ee3962471fc0ee771ec051ec

View on Chainz ↗

Height

#403,166

Difficulty

10.432902

Transactions

Size

204 B

Version

Bits

0a6ed2a8

Nonce

24,725

Timestamp

2/13/2014, 11:31:04 PM

Confirmations

6,407,937

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

9283257516749f6e3e4ad585b4df4fae5c3d00c892c88b11323f2b2b47ffebf7

Transactions (1)

Coinbase9283257516749f…3f2b2b47ffebf7

1 in → 1 out9.1700 XPM116 B

AbwWkWZt…kawDhufa

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.

1.386 × 10⁹¹(92-digit number)

13869153640946021919…03072922185420564361

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

1.386 × 10⁹¹(92-digit number)

13869153640946021919…03072922185420564361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.773 × 10⁹¹(92-digit number)

27738307281892043838…06145844370841128721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.547 × 10⁹¹(92-digit number)

55476614563784087676…12291688741682257441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.109 × 10⁹²(93-digit number)

11095322912756817535…24583377483364514881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.219 × 10⁹²(93-digit number)

22190645825513635070…49166754966729029761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.438 × 10⁹²(93-digit number)

44381291651027270140…98333509933458059521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.876 × 10⁹²(93-digit number)

88762583302054540281…96667019866916119041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.775 × 10⁹³(94-digit number)

17752516660410908056…93334039733832238081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.550 × 10⁹³(94-digit number)

35505033320821816112…86668079467664476161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

7.101 × 10⁹³(94-digit number)

71010066641643632225…73336158935328952321

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

Block #403,166

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