Block #286,027

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/30/2013, 5:46:08 PM · Difficulty 9.9851 · 6,508,923 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d35c2dd0a9a5972107acd0270ae0dc6c31a69530034c06602eda590d374bb5a5

View on Chainz ↗

Height

#286,027

Difficulty

9.985058

Transactions

Size

937 B

Version

Bits

09fc2cc2

Nonce

9,860

Timestamp

11/30/2013, 5:46:08 PM

Confirmations

6,508,923

Mined by

⛏️ KAYcLTeXRXcXHePDnP5p1bevW8AbscgPops

Merkle Root

b6c3be014d75e726223e7eb44ee538f4723034a9526501059a932b958f2fa899

Transactions (1)

Coinbaseb6c3be014d75e7…932b958f2fa899

1 in → 23 out10.0100 XPM845 B

AYcLTeXR…bscgPops AFqKfjez…qX9Ace3g AHuJ9wYh…BGmgHrKZ AQwRN8bE…V8PsTcY9 AGqQ4WX6…HCR8xUMa

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.

6.277 × 10⁹⁸(99-digit number)

62779492516052216676…09382323104274134721

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

6.277 × 10⁹⁸(99-digit number)

62779492516052216676…09382323104274134721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.255 × 10⁹⁹(100-digit number)

12555898503210443335…18764646208548269441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.511 × 10⁹⁹(100-digit number)

25111797006420886670…37529292417096538881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.022 × 10⁹⁹(100-digit number)

50223594012841773340…75058584834193077761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.004 × 10¹⁰⁰(101-digit number)

10044718802568354668…50117169668386155521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.008 × 10¹⁰⁰(101-digit number)

20089437605136709336…00234339336772311041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.017 × 10¹⁰⁰(101-digit number)

40178875210273418672…00468678673544622081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.035 × 10¹⁰⁰(101-digit number)

80357750420546837345…00937357347089244161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.607 × 10¹⁰¹(102-digit number)

16071550084109367469…01874714694178488321

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