Block #444,695

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/15/2014, 10:09:15 AM · Difficulty 10.3494 · 6,350,847 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2cd32604c3d1403023c5fd9d5a2a621ca402e5482579d3da691bf9965e5eaff8

View on Chainz ↗

Height

#444,695

Difficulty

10.349446

Transactions

Size

968 B

Version

Bits

0a597552

Nonce

28,868

Timestamp

3/15/2014, 10:09:15 AM

Confirmations

6,350,847

Mined by

⛏️ aS$&KAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

276e7fdccd6525b6c75b087da58037968ee25f6605f28a6aa7da883a37d6f4f9

Transactions (1)

Coinbase276e7fdccd6525…da883a37d6f4f9

1 in → 24 out9.3200 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ATKK7iFz…wZm46KN1 AQ8QAT3J…rCFKuVbR AGKhfQo2…h7fBXLX6

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.

1.278 × 10⁹³(94-digit number)

12783640123379156296…82206874513723901439

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

1.278 × 10⁹³(94-digit number)

12783640123379156296…82206874513723901439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.556 × 10⁹³(94-digit number)

25567280246758312592…64413749027447802879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.113 × 10⁹³(94-digit number)

51134560493516625184…28827498054895605759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.022 × 10⁹⁴(95-digit number)

10226912098703325036…57654996109791211519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.045 × 10⁹⁴(95-digit number)

20453824197406650073…15309992219582423039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.090 × 10⁹⁴(95-digit number)

40907648394813300147…30619984439164846079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.181 × 10⁹⁴(95-digit number)

81815296789626600295…61239968878329692159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.636 × 10⁹⁵(96-digit number)

16363059357925320059…22479937756659384319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.272 × 10⁹⁵(96-digit number)

32726118715850640118…44959875513318768639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.545 × 10⁹⁵(96-digit number)

65452237431701280236…89919751026637537279

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