Block #222,587

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/22/2013, 8:26:10 AM · Difficulty 9.9395 · 6,581,310 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

1f1ff3bbac002084a9965ff9848a60c5f4944c524484927f5cf3707ab7a42f45

View on Chainz ↗

Height

#222,587

Difficulty

9.939513

Transactions

Size

1.14 KB

Version

Bits

09f083e6

Nonce

304,406

Timestamp

10/22/2013, 8:26:10 AM

Confirmations

6,581,310

Mined by

⛏️ {eRf5HASQjQCtGcztA4JB1tDDTREdDA3LMRQkLKB

Merkle Root

b7a564da5f600a5366fbad2a7a7eddf81b23f89ce4568b0ced5adc597b958b83

Transactions (1)

Coinbaseb7a564da5f600a…5adc597b958b83

1 in → 30 out10.0900 XPM1.06 KB

ASQjQCtG…LMRQkLKB AeZmMFY8…mjAy5Mi4 AKXeSXzu…yeuNjvhB AScCYXya…oAz38X3p AKDTDDtx…iqvw9cdY

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.

7.485 × 10⁹³(94-digit number)

74858746812579036793…13843327964709537281

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

7.485 × 10⁹³(94-digit number)

74858746812579036793…13843327964709537281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.497 × 10⁹⁴(95-digit number)

14971749362515807358…27686655929419074561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.994 × 10⁹⁴(95-digit number)

29943498725031614717…55373311858838149121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.988 × 10⁹⁴(95-digit number)

59886997450063229435…10746623717676298241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.197 × 10⁹⁵(96-digit number)

11977399490012645887…21493247435352596481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.395 × 10⁹⁵(96-digit number)

23954798980025291774…42986494870705192961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.790 × 10⁹⁵(96-digit number)

47909597960050583548…85972989741410385921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.581 × 10⁹⁵(96-digit number)

95819195920101167096…71945979482820771841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.916 × 10⁹⁶(97-digit number)

19163839184020233419…43891958965641543681

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer