Block #12,186

1CCLength 7★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/11/2013, 9:05:58 AM · Difficulty 7.7505 · 6,782,407 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

8018f0948eadd63833b55e3ebf5f604bd48ce95b1df9fbb574ffd2d0920cd426

View on Chainz ↗

Height

#12,186

Difficulty

7.750534

Transactions

Size

196 B

Version

Bits

07c02300

Nonce

266

Timestamp

7/11/2013, 9:05:58 AM

Confirmations

6,782,407

Mined by

⛏️ P2SHAcjhaVoWPPShdSp4K3fBKNtTx1hAPjZTBV

Merkle Root

f7ee381602872bfc47121dd354dc025813fa406dc603ef0b3590a583f0f37c2b

Transactions (1)

Coinbasef7ee381602872b…90a583f0f37c2b

1 in → 1 out16.6300 XPM108 B

AcjhaVoW…hAPjZTBV

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.

7.851 × 10⁸⁹(90-digit number)

78517739638067306086…63790664198049730499

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

7.851 × 10⁸⁹(90-digit number)

78517739638067306086…63790664198049730499

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.570 × 10⁹⁰(91-digit number)

15703547927613461217…27581328396099460999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.140 × 10⁹⁰(91-digit number)

31407095855226922434…55162656792198921999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.281 × 10⁹⁰(91-digit number)

62814191710453844868…10325313584397843999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.256 × 10⁹¹(92-digit number)

12562838342090768973…20650627168795687999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.512 × 10⁹¹(92-digit number)

25125676684181537947…41301254337591375999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.025 × 10⁹¹(92-digit number)

50251353368363075895…82602508675182751999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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