Block #447,476

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/17/2014, 7:39:04 AM · Difficulty 10.3567 · 6,348,713 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

1ff9e341ec4683e91e7ed02abdfbc86777aad1dc4f8665e38b49d4b374bc604f

View on Chainz ↗

Height

#447,476

Difficulty

10.356732

Transactions

Size

970 B

Version

Bits

0a5b52c8

Nonce

186,556

Timestamp

3/17/2014, 7:39:04 AM

Confirmations

6,348,713

Mined by

⛏️ aS&AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

da3d0a24624703fee530477058352b6639b2eb9dcffc6af54d8fd4644b04852f

Transactions (1)

Coinbaseda3d0a24624703…8fd4644b04852f

1 in → 24 out9.3100 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 AcuM7XiJ…5uND8Jce

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.

3.782 × 10⁹⁶(97-digit number)

37824150053141682274…22447912010576453119

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

3.782 × 10⁹⁶(97-digit number)

37824150053141682274…22447912010576453119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.564 × 10⁹⁶(97-digit number)

75648300106283364548…44895824021152906239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.512 × 10⁹⁷(98-digit number)

15129660021256672909…89791648042305812479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.025 × 10⁹⁷(98-digit number)

30259320042513345819…79583296084611624959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.051 × 10⁹⁷(98-digit number)

60518640085026691638…59166592169223249919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.210 × 10⁹⁸(99-digit number)

12103728017005338327…18333184338446499839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.420 × 10⁹⁸(99-digit number)

24207456034010676655…36666368676892999679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.841 × 10⁹⁸(99-digit number)

48414912068021353311…73332737353785999359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.682 × 10⁹⁸(99-digit number)

96829824136042706622…46665474707571998719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.936 × 10⁹⁹(100-digit number)

19365964827208541324…93330949415143997439

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