Block #1,316,375

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/7/2015, 2:25:14 AM · Difficulty 10.8626 · 5,487,097 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a0f585c9bbec8e30ca8d46fdddc12029bca101ea44736af70125300a4356c9b3

View on Chainz ↗

Height

#1,316,375

Difficulty

10.862571

Transactions

Size

25.23 KB

Version

Bits

0adcd16c

Nonce

646,266,244

Timestamp

11/7/2015, 2:25:14 AM

Confirmations

5,487,097

Mined by

⛏️ P2SHAbVnrcXKC525VAUMsbUCS9wht1i9bQzpT1

Merkle Root

31c6ba16177f71a6919a0fc588943c98dc1aa1ef9ff538fe7cd851d05a210485

Transactions (2)

Coinbasee0bbd681e61c3a…c5c84e5a2c02e7

1 in → 1 out8.7200 XPM110 B

AbVnrcXK…i9bQzpT1

82834ef49915c2…83d92625f18119

173 in → 1 out17.6034 XPM25.03 KB

AHJeiJjZ…AtVjQXra

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.

2.046 × 10⁹⁴(95-digit number)

20460635986149574349…83680588251769663041

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

2.046 × 10⁹⁴(95-digit number)

20460635986149574349…83680588251769663041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.092 × 10⁹⁴(95-digit number)

40921271972299148699…67361176503539326081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.184 × 10⁹⁴(95-digit number)

81842543944598297399…34722353007078652161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.636 × 10⁹⁵(96-digit number)

16368508788919659479…69444706014157304321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.273 × 10⁹⁵(96-digit number)

32737017577839318959…38889412028314608641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.547 × 10⁹⁵(96-digit number)

65474035155678637919…77778824056629217281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.309 × 10⁹⁶(97-digit number)

13094807031135727583…55557648113258434561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.618 × 10⁹⁶(97-digit number)

26189614062271455167…11115296226516869121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.237 × 10⁹⁶(97-digit number)

52379228124542910335…22230592453033738241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.047 × 10⁹⁷(98-digit number)

10475845624908582067…44461184906067476481

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