Block #187,818

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/30/2013, 7:49:28 PM · Difficulty 9.8690 · 6,606,625 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

f3a4fa09d1441431f3b082ef6c6fb33e5a8949879b381213e5095bcc67c0e49e

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Height

#187,818

Difficulty

9.868955

Transactions

Size

2.74 KB

Version

Bits

09de73dd

Nonce

1,164,736,868

Timestamp

9/30/2013, 7:49:28 PM

Confirmations

6,606,625

Mined by

⛏️ RIEAJYYHSv7evqm2NrAu8V9H7ymBQkiK98usT

Merkle Root

99a24c38ce5ec17dbb65e1ca5402ac725a9593ca0de5bcac9f24784d884067f8

Transactions (1)

Coinbase99a24c38ce5ec1…24784d884067f8

1 in → 78 out10.2300 XPM2.65 KB

AJYYHSv7…kiK98usT APxhhWVB…fH2xP7H4 AVc2sXq6…vLzcknzu AaRwgbNo…umdKrqqi ARRgSTT1…RvwKKom5

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.

5.025 × 10⁹⁶(97-digit number)

50250280633879213529…70005932918061630721

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

5.025 × 10⁹⁶(97-digit number)

50250280633879213529…70005932918061630721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.005 × 10⁹⁷(98-digit number)

10050056126775842705…40011865836123261441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.010 × 10⁹⁷(98-digit number)

20100112253551685411…80023731672246522881

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×2−1 →

2^3 × origin + 1

4.020 × 10⁹⁷(98-digit number)

40200224507103370823…60047463344493045761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.040 × 10⁹⁷(98-digit number)

80400449014206741646…20094926688986091521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.608 × 10⁹⁸(99-digit number)

16080089802841348329…40189853377972183041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.216 × 10⁹⁸(99-digit number)

32160179605682696658…80379706755944366081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.432 × 10⁹⁸(99-digit number)

64320359211365393317…60759413511888732161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.286 × 10⁹⁹(100-digit number)

12864071842273078663…21518827023777464321

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