Block #169,891

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/18/2013, 8:55:54 AM · Difficulty 9.8664 · 6,622,054 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

958a46ca5078b546dce06bf0269f64431a8f04cbeaebbe70dd139a15812b0b74

View on Chainz ↗

Height

#169,891

Difficulty

9.866440

Transactions

Size

198 B

Version

Bits

09ddcf01

Nonce

72,948

Timestamp

9/18/2013, 8:55:54 AM

Confirmations

6,622,054

Merkle Root

dd12362ad7508d6f95f5a2f6aae0cebf30537b6eb2579809303e587db7a2b80c

Transactions (1)

Coinbasedd12362ad7508d…3e587db7a2b80c

1 in → 1 out10.2600 XPM109 B

AWsEijaA…9WbDL6tH

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.

4.843 × 10⁹¹(92-digit number)

48439477030328949858…77428647735562691199

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

4.843 × 10⁹¹(92-digit number)

48439477030328949858…77428647735562691199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

9.687 × 10⁹¹(92-digit number)

96878954060657899717…54857295471125382399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.937 × 10⁹²(93-digit number)

19375790812131579943…09714590942250764799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.875 × 10⁹²(93-digit number)

38751581624263159887…19429181884501529599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.750 × 10⁹²(93-digit number)

77503163248526319774…38858363769003059199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.550 × 10⁹³(94-digit number)

15500632649705263954…77716727538006118399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.100 × 10⁹³(94-digit number)

31001265299410527909…55433455076012236799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.200 × 10⁹³(94-digit number)

62002530598821055819…10866910152024473599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.240 × 10⁹⁴(95-digit number)

12400506119764211163…21733820304048947199

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