Block #261,917

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/16/2013, 7:32:16 AM · Difficulty 9.9703 · 6,571,639 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

13c51e9adec7e5d4308bd2ae6e4ce0f0946be7d3957f37d53a66f995ccbf2b0f

View on Chainz ↗

Height

#261,917

Difficulty

9.970252

Transactions

Size

1.94 KB

Version

Bits

09f86275

Nonce

498,315

Timestamp

11/16/2013, 7:32:16 AM

Confirmations

6,571,639

Mined by

⛏️ aR4AU9KdB9rpz9LAxy9pEhEHibVcuo5XC6WMy

Merkle Root

87d4631301928123ecb3c97a0a99b7840e676375908fc899bd24ae22780902b1

Transactions (1)

Coinbase87d46313019281…24ae22780902b1

1 in → 54 out10.0200 XPM1.85 KB

AU9KdB9r…o5XC6WMy AFqKfjez…qX9Ace3g APH8rV6F…heb1HF2Z AKXeSXzu…yeuNjvhB AQapNBe8…Pxk4vkev

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.

1.370 × 10⁹⁰(91-digit number)

13709743491853083668…31567275487615971729

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

1.370 × 10⁹⁰(91-digit number)

13709743491853083668…31567275487615971729

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.741 × 10⁹⁰(91-digit number)

27419486983706167336…63134550975231943459

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.483 × 10⁹⁰(91-digit number)

54838973967412334672…26269101950463886919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.096 × 10⁹¹(92-digit number)

10967794793482466934…52538203900927773839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.193 × 10⁹¹(92-digit number)

21935589586964933868…05076407801855547679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.387 × 10⁹¹(92-digit number)

43871179173929867737…10152815603711095359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.774 × 10⁹¹(92-digit number)

87742358347859735475…20305631207422190719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.754 × 10⁹²(93-digit number)

17548471669571947095…40611262414844381439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.509 × 10⁹²(93-digit number)

35096943339143894190…81222524829688762879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.019 × 10⁹²(93-digit number)

70193886678287788380…62445049659377525759

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

Block #261,917

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