Block #19,893

1CCLength 8★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/12/2013, 10:21:10 AM · Difficulty 7.9271 · 6,783,344 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

d8c40165e5d86d9ea00d815aa196465903455cc45e098c94698794033fbd5495

View on Chainz ↗

Height

#19,893

Difficulty

7.927110

Transactions

Size

208 B

Version

Bits

07ed571a

Nonce

Timestamp

7/12/2013, 10:21:10 AM

Confirmations

6,783,344

Mined by

⛏️ P2SHALtQiCynzfouqbRxJ6ViGNCLqY68VU6xPK

Merkle Root

b6330b3342d73f4831332a87e1aa35a01c9dc8bffa506b33ee8fe18b3d2491c7

Transactions (1)

Coinbaseb6330b3342d73f…8fe18b3d2491c7

1 in → 1 out15.8900 XPM108 B

ALtQiCyn…68VU6xPK

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.

7.274 × 10¹¹⁷(118-digit number)

72749947984875284208…96389461448325393299

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

7.274 × 10¹¹⁷(118-digit number)

72749947984875284208…96389461448325393299

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.454 × 10¹¹⁸(119-digit number)

14549989596975056841…92778922896650786599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.909 × 10¹¹⁸(119-digit number)

29099979193950113683…85557845793301573199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.819 × 10¹¹⁸(119-digit number)

58199958387900227366…71115691586603146399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.163 × 10¹¹⁹(120-digit number)

11639991677580045473…42231383173206292799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.327 × 10¹¹⁹(120-digit number)

23279983355160090946…84462766346412585599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.655 × 10¹¹⁹(120-digit number)

46559966710320181893…68925532692825171199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.311 × 10¹¹⁹(120-digit number)

93119933420640363786…37851065385650342399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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