Block #186,669

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/30/2013, 1:13:04 AM · Difficulty 9.8670 · 6,618,376 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b3bb4cf83514b2ecca572730d209c81d9444093a4e6a40183085da0f4cf0eb6a

View on Chainz ↗

Height

#186,669

Difficulty

9.866963

Transactions

Size

1.57 KB

Version

Bits

09ddf14c

Nonce

1,164,744,149

Timestamp

9/30/2013, 1:13:04 AM

Confirmations

6,618,376

Mined by

⛏️ -RHAVx4MCjhvLM2SGEKnqAitwMFYvFiFXiyuD

Merkle Root

adb40a3b5a34c07d55128444885bd3067b353aa6efc5fb6a2ab198c1c3734536

Transactions (1)

Coinbaseadb40a3b5a34c0…b198c1c3734536

1 in → 43 out10.2500 XPM1.49 KB

AVx4MCjh…FiFXiyuD AVeHc9d8…MRstqd4p AWgwrQ5r…KVAzQwZ1 AJErs5Nt…zQVnq9U2 AJCCNvEZ…gX1b1gmx

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.

6.976 × 10⁸⁸(89-digit number)

69760530923030451422…34968574714639402699

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

6.976 × 10⁸⁸(89-digit number)

69760530923030451422…34968574714639402699

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.395 × 10⁸⁹(90-digit number)

13952106184606090284…69937149429278805399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.790 × 10⁸⁹(90-digit number)

27904212369212180568…39874298858557610799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.580 × 10⁸⁹(90-digit number)

55808424738424361137…79748597717115221599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.116 × 10⁹⁰(91-digit number)

11161684947684872227…59497195434230443199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.232 × 10⁹⁰(91-digit number)

22323369895369744455…18994390868460886399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.464 × 10⁹⁰(91-digit number)

44646739790739488910…37988781736921772799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.929 × 10⁹⁰(91-digit number)

89293479581478977820…75977563473843545599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.785 × 10⁹¹(92-digit number)

17858695916295795564…51955126947687091199

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