Block #311,672

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/14/2013, 4:22:05 PM · Difficulty 9.9956 · 6,484,277 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2807518c1596baca10d2fad60c5ab112ef10d4a1ea4a28391e94973c0d85e970

View on Chainz ↗

Height

#311,672

Difficulty

9.995559

Transactions

Size

935 B

Version

Bits

09fedcf9

Nonce

292,926

Timestamp

12/14/2013, 4:22:05 PM

Confirmations

6,484,277

Mined by

⛏️ xaRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

01c0c786cf9bca90042086f3ac26aad1c143f3b60f5fe111e166f448543f6d80

Transactions (1)

Coinbase01c0c786cf9bca…66f448543f6d80

1 in → 23 out9.9900 XPM845 B

Aac9Hjdg…P4ktypc3 APeshfYV…3PKcKMKH AKzkYQaQ…zR4FspJZ AcC2zSod…rtWatH79 Aaf3yuJg…fCrhFXXe

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.

7.169 × 10⁹³(94-digit number)

71693926687572507344…96441715723772108801

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

7.169 × 10⁹³(94-digit number)

71693926687572507344…96441715723772108801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.433 × 10⁹⁴(95-digit number)

14338785337514501468…92883431447544217601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.867 × 10⁹⁴(95-digit number)

28677570675029002937…85766862895088435201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.735 × 10⁹⁴(95-digit number)

57355141350058005875…71533725790176870401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.147 × 10⁹⁵(96-digit number)

11471028270011601175…43067451580353740801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.294 × 10⁹⁵(96-digit number)

22942056540023202350…86134903160707481601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.588 × 10⁹⁵(96-digit number)

45884113080046404700…72269806321414963201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.176 × 10⁹⁵(96-digit number)

91768226160092809400…44539612642829926401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.835 × 10⁹⁶(97-digit number)

18353645232018561880…89079225285659852801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.670 × 10⁹⁶(97-digit number)

36707290464037123760…78158450571319705601

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