Block #66,053

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/19/2013, 3:28:48 PM · Difficulty 8.9854 · 6,744,163 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ce0da9bdbf307c410894d6b2340d80a7e7e1c2986ebfb1cebb69b852ccf4b876

View on Chainz ↗

Height

#66,053

Difficulty

8.985421

Transactions

Size

871 B

Version

Bits

08fc4494

Nonce

435

Timestamp

7/19/2013, 3:28:48 PM

Confirmations

6,744,163

Mined by

⛏️ P2SHAQnRRkZosSyyk3WtrF31ZEzETUxUGud2Wa

Merkle Root

b47ffce1dfcb55169e4b3a8c1f9b7e29ff3c257d89aa6992be2b346747c847bc

Transactions (2)

Coinbase0e02e2a21fad44…da20b6fbe0cde4

1 in → 1 out12.3800 XPM110 B

AQnRRkZo…xUGud2Wa

0cc092ec8fd00e…87abc681f75056

4 in → 2 out1000.4200 XPM670 B

Ac3ZdZXv…CGGh1Yer AH3C69ei…yj9SuS7P

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.

2.373 × 10⁹⁸(99-digit number)

23731618265222303704…87919697620507640679

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

2.373 × 10⁹⁸(99-digit number)

23731618265222303704…87919697620507640679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.746 × 10⁹⁸(99-digit number)

47463236530444607409…75839395241015281359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.492 × 10⁹⁸(99-digit number)

94926473060889214819…51678790482030562719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.898 × 10⁹⁹(100-digit number)

18985294612177842963…03357580964061125439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.797 × 10⁹⁹(100-digit number)

37970589224355685927…06715161928122250879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.594 × 10⁹⁹(100-digit number)

75941178448711371855…13430323856244501759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.518 × 10¹⁰⁰(101-digit number)

15188235689742274371…26860647712489003519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.037 × 10¹⁰⁰(101-digit number)

30376471379484548742…53721295424978007039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.075 × 10¹⁰⁰(101-digit number)

60752942758969097484…07442590849956014079

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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

Block #66,053

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