Block #335,821

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/30/2013, 12:52:19 PM · Difficulty 10.1429 · 6,465,169 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f24210c99a4137c45960b61b96ff776cd75dcd1ca7b549c877b6ee9810ac9205

View on Chainz ↗

Height

#335,821

Difficulty

10.142934

Transactions

Size

1.01 KB

Version

Bits

0a249755

Nonce

4,920

Timestamp

12/30/2013, 12:52:19 PM

Confirmations

6,465,169

Mined by

⛏️ aRlzAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

5a064a9b7653f773d2f5025a164889377afe75bb0a42ff7089d20bc4f5863e03

Transactions (1)

Coinbase5a064a9b7653f7…d20bc4f5863e03

1 in → 26 out9.7100 XPM946 B

Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz AG5YAjec…VhA4Aeh1 AFutDVqJ…TJTJj6UF

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.

8.799 × 10¹⁰⁰(101-digit number)

87990795435710281477…03337288375187537919

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

8.799 × 10¹⁰⁰(101-digit number)

87990795435710281477…03337288375187537919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.759 × 10¹⁰¹(102-digit number)

17598159087142056295…06674576750375075839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.519 × 10¹⁰¹(102-digit number)

35196318174284112591…13349153500750151679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.039 × 10¹⁰¹(102-digit number)

70392636348568225182…26698307001500303359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.407 × 10¹⁰²(103-digit number)

14078527269713645036…53396614003000606719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.815 × 10¹⁰²(103-digit number)

28157054539427290072…06793228006001213439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.631 × 10¹⁰²(103-digit number)

56314109078854580145…13586456012002426879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.126 × 10¹⁰³(104-digit number)

11262821815770916029…27172912024004853759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.252 × 10¹⁰³(104-digit number)

22525643631541832058…54345824048009707519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.505 × 10¹⁰³(104-digit number)

45051287263083664116…08691648096019415039

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