Block #64,241

1CCLength 8★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/19/2013, 6:28:09 AM · Difficulty 8.9812 · 6,728,534 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

4d76e65ac8fc8a7b23ba7937aafc7c3e841ef336c49e596b980669136309d89b

View on Chainz ↗

Height

#64,241

Difficulty

8.981173

Transactions

Size

203 B

Version

Bits

08fb2e24

Nonce

834

Timestamp

7/19/2013, 6:28:09 AM

Confirmations

6,728,534

Merkle Root

044286e55225823007df21654e40412373697626c7501a89394c1a8449775b2d

Transactions (1)

Coinbase044286e5522582…4c1a8449775b2d

1 in → 1 out12.3800 XPM110 B

AXWphP8T…4trwmtBM

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.

1.386 × 10¹⁰³(104-digit number)

13865177227206777736…40950674203855607999

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

1.386 × 10¹⁰³(104-digit number)

13865177227206777736…40950674203855607999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.773 × 10¹⁰³(104-digit number)

27730354454413555472…81901348407711215999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.546 × 10¹⁰³(104-digit number)

55460708908827110944…63802696815422431999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.109 × 10¹⁰⁴(105-digit number)

11092141781765422188…27605393630844863999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.218 × 10¹⁰⁴(105-digit number)

22184283563530844377…55210787261689727999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.436 × 10¹⁰⁴(105-digit number)

44368567127061688755…10421574523379455999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.873 × 10¹⁰⁴(105-digit number)

88737134254123377511…20843149046758911999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.774 × 10¹⁰⁵(106-digit number)

17747426850824675502…41686298093517823999

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