Block #440,939

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/12/2014, 6:38:02 PM · Difficulty 10.3540 · 6,353,913 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

09887e5c3e88937331bf3fa1958b5c4cb177ab0272915b130a319b73ba8cb89a

View on Chainz ↗

Height

#440,939

Difficulty

10.354029

Transactions

Size

578 B

Version

Bits

0a5aa1a1

Nonce

18,025

Timestamp

3/12/2014, 6:38:02 PM

Confirmations

6,353,913

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

a89bbe98262b92b5db32dbb89e6748000669630db28630f114273062f0d3f558

Transactions (2)

Coinbase8bc2a9d4cde854…e138c4f00d4cc6

1 in → 1 out9.3200 XPM116 B

AbwWkWZt…kawDhufa

d4c22d3448cbb6…18ffe7229ffb98

2 in → 2 out6.0910 XPM371 B

AGhqx9U2…jxFM6Bm6 AMit4w3p…TwJjgNSJ

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.

1.783 × 10⁹⁷(98-digit number)

17834482260297433312…75501937677791517459

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

1.783 × 10⁹⁷(98-digit number)

17834482260297433312…75501937677791517459

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.566 × 10⁹⁷(98-digit number)

35668964520594866624…51003875355583034919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.133 × 10⁹⁷(98-digit number)

71337929041189733249…02007750711166069839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.426 × 10⁹⁸(99-digit number)

14267585808237946649…04015501422332139679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.853 × 10⁹⁸(99-digit number)

28535171616475893299…08031002844664279359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.707 × 10⁹⁸(99-digit number)

57070343232951786599…16062005689328558719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.141 × 10⁹⁹(100-digit number)

11414068646590357319…32124011378657117439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.282 × 10⁹⁹(100-digit number)

22828137293180714639…64248022757314234879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.565 × 10⁹⁹(100-digit number)

45656274586361429279…28496045514628469759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

9.131 × 10⁹⁹(100-digit number)

91312549172722858559…56992091029256939519

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