Block #314,947

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/16/2013, 6:17:09 AM · Difficulty 10.0791 · 6,494,964 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e0b4e497fa97f2d82bbbb4f9fbedc5475d040a96da73b6153a856e9c35dd83d8

View on Chainz ↗

Height

#314,947

Difficulty

10.079142

Transactions

Size

208 B

Version

Bits

0a1442a4

Nonce

98,724

Timestamp

12/16/2013, 6:17:09 AM

Confirmations

6,494,964

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

182f8b627da24503b766a130e8306c6b25dfa78ca89c06ba35d0b5c5b370be3a

Transactions (1)

Coinbase182f8b627da245…d0b5c5b370be3a

1 in → 1 out9.8300 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.

9.677 × 10⁹⁹(100-digit number)

96771693199246264003…51844897120461521921

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

9.677 × 10⁹⁹(100-digit number)

96771693199246264003…51844897120461521921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.935 × 10¹⁰⁰(101-digit number)

19354338639849252800…03689794240923043841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.870 × 10¹⁰⁰(101-digit number)

38708677279698505601…07379588481846087681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.741 × 10¹⁰⁰(101-digit number)

77417354559397011202…14759176963692175361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.548 × 10¹⁰¹(102-digit number)

15483470911879402240…29518353927384350721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.096 × 10¹⁰¹(102-digit number)

30966941823758804481…59036707854768701441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.193 × 10¹⁰¹(102-digit number)

61933883647517608962…18073415709537402881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.238 × 10¹⁰²(103-digit number)

12386776729503521792…36146831419074805761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.477 × 10¹⁰²(103-digit number)

24773553459007043584…72293662838149611521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.954 × 10¹⁰²(103-digit number)

49547106918014087169…44587325676299223041

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 #314,947

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