Block #267,221

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/21/2013, 2:49:03 AM · Difficulty 9.9593 · 6,524,469 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

d19bd6894471b50e6bd9b5bb1091f7f769cd724b3ae76face85ab4da4e0888c2

View on Chainz ↗

Height

#267,221

Difficulty

9.959292

Transactions

Size

427 B

Version

Bits

09f59430

Nonce

80,531

Timestamp

11/21/2013, 2:49:03 AM

Confirmations

6,524,469

Merkle Root

c8ff5ddf9baecf4807e861bdbd7aaa4a43ed3fab5fd35f379c33e59c17f54037

Transactions (2)

Coinbasec6c412406f71e7…655d9b540bf435

1 in → 1 out10.0800 XPM110 B

AeKNrjNj…1NEq95Ta

37d6f8d575c579…383f8f1c8f3e67

1 in → 2 out3.3655 XPM226 B

ARC3GLtb…BSXvSmKg AeKNrjNj…1NEq95Ta

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.

1.088 × 10⁹⁷(98-digit number)

10883285767395428435…36039861175939658239

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

1.088 × 10⁹⁷(98-digit number)

10883285767395428435…36039861175939658239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.176 × 10⁹⁷(98-digit number)

21766571534790856870…72079722351879316479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.353 × 10⁹⁷(98-digit number)

43533143069581713740…44159444703758632959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.706 × 10⁹⁷(98-digit number)

87066286139163427481…88318889407517265919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.741 × 10⁹⁸(99-digit number)

17413257227832685496…76637778815034531839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.482 × 10⁹⁸(99-digit number)

34826514455665370992…53275557630069063679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.965 × 10⁹⁸(99-digit number)

69653028911330741985…06551115260138127359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.393 × 10⁹⁹(100-digit number)

13930605782266148397…13102230520276254719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.786 × 10⁹⁹(100-digit number)

27861211564532296794…26204461040552509439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.572 × 10⁹⁹(100-digit number)

55722423129064593588…52408922081105018879

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