Block #186,114

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/29/2013, 5:35:34 PM · Difficulty 9.8643 · 6,604,947 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

dcd9932f3c3f9b0e324de1d17510b2caa66c7787422b0f8817055160edffcfc8

View on Chainz ↗

Height

#186,114

Difficulty

9.864257

Transactions

Size

210 B

Version

Bits

09dd3ff1

Nonce

430,686

Timestamp

9/29/2013, 5:35:34 PM

Confirmations

6,604,947

Merkle Root

bd84a18bd98890ddd693a7ac54671e8f949aff4e798dd5dfbc3e06bbb2ab50c0

Transactions (1)

Coinbasebd84a18bd98890…3e06bbb2ab50c0

1 in → 1 out10.2600 XPM116 B

AcLBm5Z9…S683d7c3

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.

3.188 × 10¹⁰⁵(106-digit number)

31889215568811330795…23852133509052825601

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

3.188 × 10¹⁰⁵(106-digit number)

31889215568811330795…23852133509052825601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.377 × 10¹⁰⁵(106-digit number)

63778431137622661591…47704267018105651201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.275 × 10¹⁰⁶(107-digit number)

12755686227524532318…95408534036211302401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.551 × 10¹⁰⁶(107-digit number)

25511372455049064636…90817068072422604801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.102 × 10¹⁰⁶(107-digit number)

51022744910098129272…81634136144845209601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.020 × 10¹⁰⁷(108-digit number)

10204548982019625854…63268272289690419201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.040 × 10¹⁰⁷(108-digit number)

20409097964039251709…26536544579380838401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.081 × 10¹⁰⁷(108-digit number)

40818195928078503418…53073089158761676801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.163 × 10¹⁰⁷(108-digit number)

81636391856157006836…06146178317523353601

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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