Block #438,983

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/11/2014, 9:20:16 AM · Difficulty 10.3577 · 6,367,332 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6c271f85ad4246f5b6b5ea24e76b3e9bc2201d0d8552a2065b5da7230cf13b03

View on Chainz ↗

Height

#438,983

Difficulty

10.357698

Transactions

Size

865 B

Version

Bits

0a5b9220

Nonce

21,244

Timestamp

3/11/2014, 9:20:16 AM

Confirmations

6,367,332

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

e05be2082994a7e58af9995aecb20f93390d13d9daf6e9f237c22abe92d7cd64

Transactions (1)

Coinbasee05be2082994a7…c22abe92d7cd64

1 in → 21 out9.3100 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AUzEPJFG…kYkA5U9V ASgUri65…C7NLcyBg AQT6GR3K…nYGow82m

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.

6.042 × 10⁸⁹(90-digit number)

60421734864928022094…62707194382930250329

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

6.042 × 10⁸⁹(90-digit number)

60421734864928022094…62707194382930250329

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.208 × 10⁹⁰(91-digit number)

12084346972985604418…25414388765860500659

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.416 × 10⁹⁰(91-digit number)

24168693945971208837…50828777531721001319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.833 × 10⁹⁰(91-digit number)

48337387891942417675…01657555063442002639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.667 × 10⁹⁰(91-digit number)

96674775783884835351…03315110126884005279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.933 × 10⁹¹(92-digit number)

19334955156776967070…06630220253768010559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.866 × 10⁹¹(92-digit number)

38669910313553934140…13260440507536021119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.733 × 10⁹¹(92-digit number)

77339820627107868280…26520881015072042239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.546 × 10⁹²(93-digit number)

15467964125421573656…53041762030144084479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.093 × 10⁹²(93-digit number)

30935928250843147312…06083524060288168959

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

Block #438,983

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