Block #445,293

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/15/2014, 7:22:20 PM · Difficulty 10.3555 · 6,359,906 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bb9a1fa102018062047e67fdf7c2e09a171fde95cc7d4c69bd397676895dd9c8

View on Chainz ↗

Height

#445,293

Difficulty

10.355452

Transactions

Size

901 B

Version

Bits

0a5afeee

Nonce

107,816

Timestamp

3/15/2014, 7:22:20 PM

Confirmations

6,359,906

Mined by

⛏️ maS$BAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

a50e362ca326e5ca48b448c53ca1651bec4bc21a5557088d67668d85abc1e49e

Transactions (1)

Coinbasea50e362ca326e5…668d85abc1e49e

1 in → 22 out9.3006 XPM811 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 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.

1.901 × 10⁹⁵(96-digit number)

19013067415405058848…92764228446180440319

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

1.901 × 10⁹⁵(96-digit number)

19013067415405058848…92764228446180440319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.802 × 10⁹⁵(96-digit number)

38026134830810117697…85528456892360880639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.605 × 10⁹⁵(96-digit number)

76052269661620235395…71056913784721761279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.521 × 10⁹⁶(97-digit number)

15210453932324047079…42113827569443522559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.042 × 10⁹⁶(97-digit number)

30420907864648094158…84227655138887045119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.084 × 10⁹⁶(97-digit number)

60841815729296188316…68455310277774090239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.216 × 10⁹⁷(98-digit number)

12168363145859237663…36910620555548180479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.433 × 10⁹⁷(98-digit number)

24336726291718475326…73821241111096360959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.867 × 10⁹⁷(98-digit number)

48673452583436950653…47642482222192721919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

9.734 × 10⁹⁷(98-digit number)

97346905166873901306…95284964444385443839

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