Block #312,202

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/14/2013, 10:04:05 PM · Difficulty 9.9957 · 6,482,850 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

548e0bd351473e328b2b50f6875aa24479d3eedf3b1c86a7cc481e8e1a54e8ec

View on Chainz ↗

Height

#312,202

Difficulty

9.995737

Transactions

Size

1.11 KB

Version

Bits

09fee89f

Nonce

105,301

Timestamp

12/14/2013, 10:04:05 PM

Confirmations

6,482,850

Mined by

⛏️ aR=Aac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

9baeed7ad558456b9fd9d11937adbba70e17c0833247521113f317136eb669c7

Transactions (1)

Coinbase9baeed7ad55845…f317136eb669c7

1 in → 29 out9.9700 XPM1.02 KB

Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz AQwRN8bE…V8PsTcY9 AYtDvcGs…VuAcA7m7 AKzkYQaQ…zR4FspJZ

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.

4.885 × 10⁹²(93-digit number)

48855717333841140427…15735963436045194239

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

4.885 × 10⁹²(93-digit number)

48855717333841140427…15735963436045194239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

9.771 × 10⁹²(93-digit number)

97711434667682280854…31471926872090388479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.954 × 10⁹³(94-digit number)

19542286933536456170…62943853744180776959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.908 × 10⁹³(94-digit number)

39084573867072912341…25887707488361553919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.816 × 10⁹³(94-digit number)

78169147734145824683…51775414976723107839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.563 × 10⁹⁴(95-digit number)

15633829546829164936…03550829953446215679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.126 × 10⁹⁴(95-digit number)

31267659093658329873…07101659906892431359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.253 × 10⁹⁴(95-digit number)

62535318187316659746…14203319813784862719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.250 × 10⁹⁵(96-digit number)

12507063637463331949…28406639627569725439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.501 × 10⁹⁵(96-digit number)

25014127274926663898…56813279255139450879

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer