Block #223,842

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/23/2013, 8:17:45 AM · Difficulty 9.9374 · 6,591,262 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

c7483e4005e9331380ebf3e130ba2225d08701915633f551ce7156ef382a1261

View on Chainz ↗

Height

#223,842

Difficulty

9.937371

Transactions

Size

197 B

Version

Bits

09eff794

Nonce

297,079

Timestamp

10/23/2013, 8:17:45 AM

Confirmations

6,591,262

Mined by

⛏️ P2SHATRnMoWiPfLU4bA2TUCHsxS8iKZP2o2dcV

Merkle Root

c0b3b52c2ee80c08c640be2bc53d1fd7c65f5a8acf6ccaf6f8ca97c43ca1f5d1

Transactions (1)

Coinbasec0b3b52c2ee80c…ca97c43ca1f5d1

1 in → 1 out10.1100 XPM109 B

ATRnMoWi…ZP2o2dcV

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.

7.850 × 10⁹⁰(91-digit number)

78501943868065371324…36683389101527208519

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

7.850 × 10⁹⁰(91-digit number)

78501943868065371324…36683389101527208519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.570 × 10⁹¹(92-digit number)

15700388773613074264…73366778203054417039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.140 × 10⁹¹(92-digit number)

31400777547226148529…46733556406108834079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.280 × 10⁹¹(92-digit number)

62801555094452297059…93467112812217668159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.256 × 10⁹²(93-digit number)

12560311018890459411…86934225624435336319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.512 × 10⁹²(93-digit number)

25120622037780918823…73868451248870672639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.024 × 10⁹²(93-digit number)

50241244075561837647…47736902497741345279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.004 × 10⁹³(94-digit number)

10048248815112367529…95473804995482690559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.009 × 10⁹³(94-digit number)

20096497630224735059…90947609990965381119

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 #223,842

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