Block #302,324

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/9/2013, 6:09:02 PM · Difficulty 9.9927 · 6,492,013 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

f2db4315b8679cd21a44cd53faaa4860bcc9893891d1be232a27c2ff246980ef

View on Chainz ↗

Height

#302,324

Difficulty

9.992684

Transactions

Size

937 B

Version

Bits

09fe2089

Nonce

22,879

Timestamp

12/9/2013, 6:09:02 PM

Confirmations

6,492,013

Merkle Root

7a9bb9529e99e9f5a6ccdbf3b1689a6398fd788112ad4132f856be4840315ce1

Transactions (1)

Coinbase7a9bb9529e99e9…56be4840315ce1

1 in → 23 out10.0000 XPM845 B

AQwRN8bE…V8PsTcY9 AG35cSDg…jNDNzTuM AWZd1qVJ…9pj9yfPa AcM3ext6…Hwtj9Qp3 ARW1RY2f…qHYBGJdu

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.

1.158 × 10⁹⁹(100-digit number)

11583389226946743178…95632559806119482801

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

1.158 × 10⁹⁹(100-digit number)

11583389226946743178…95632559806119482801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.316 × 10⁹⁹(100-digit number)

23166778453893486356…91265119612238965601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.633 × 10⁹⁹(100-digit number)

46333556907786972713…82530239224477931201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.266 × 10⁹⁹(100-digit number)

92667113815573945427…65060478448955862401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.853 × 10¹⁰⁰(101-digit number)

18533422763114789085…30120956897911724801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.706 × 10¹⁰⁰(101-digit number)

37066845526229578170…60241913795823449601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.413 × 10¹⁰⁰(101-digit number)

74133691052459156341…20483827591646899201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.482 × 10¹⁰¹(102-digit number)

14826738210491831268…40967655183293798401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.965 × 10¹⁰¹(102-digit number)

29653476420983662536…81935310366587596801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.930 × 10¹⁰¹(102-digit number)

59306952841967325073…63870620733175193601

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