Block #344,445

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/5/2014, 7:51:50 AM · Difficulty 10.1921 · 6,453,245 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

cd103b26defae9d2de067a650232382f7a5cb905176e3cb729a168a421993165

View on Chainz ↗

Height

#344,445

Difficulty

10.192139

Transactions

Size

1.08 KB

Version

Bits

0a313003

Nonce

38,651

Timestamp

1/5/2014, 7:51:50 AM

Confirmations

6,453,245

Mined by

⛏️ }AaRPAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e824728840262926d675c83bf7dc3c14e6ca9a0f8ea421671aeae7aac9e7ae13

Transactions (1)

Coinbasee8247288402629…eae7aac9e7ae13

1 in → 28 out9.5900 XPM1015 B

AQvZBsUo…hppgRZTJ AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz AL8CJrXc…ReWqhicJ Af5qanha…3S4JZCTK

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.

5.326 × 10⁹⁶(97-digit number)

53260718336926449012…23807810129161591199

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

5.326 × 10⁹⁶(97-digit number)

53260718336926449012…23807810129161591199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.065 × 10⁹⁷(98-digit number)

10652143667385289802…47615620258323182399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.130 × 10⁹⁷(98-digit number)

21304287334770579605…95231240516646364799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.260 × 10⁹⁷(98-digit number)

42608574669541159210…90462481033292729599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.521 × 10⁹⁷(98-digit number)

85217149339082318420…80924962066585459199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.704 × 10⁹⁸(99-digit number)

17043429867816463684…61849924133170918399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.408 × 10⁹⁸(99-digit number)

34086859735632927368…23699848266341836799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.817 × 10⁹⁸(99-digit number)

68173719471265854736…47399696532683673599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.363 × 10⁹⁹(100-digit number)

13634743894253170947…94799393065367347199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.726 × 10⁹⁹(100-digit number)

27269487788506341894…89598786130734694399

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