Block #241,190

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/3/2013, 1:34:46 AM · Difficulty 9.9577 · 6,589,356 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

9fd15aebd48985ed3e263453271395977e5f09a7bc55d208ba94fc043e487f79

View on Chainz ↗

Height

#241,190

Difficulty

9.957695

Transactions

Size

1.54 KB

Version

Bits

09f52b7d

Nonce

130,473

Timestamp

11/3/2013, 1:34:46 AM

Confirmations

6,589,356

Mined by

⛏️ &RuARXSrG7zDJaFCruTxsaP6YvsvPCRW69WR4

Merkle Root

6a703d83e5cfcab6f40294ba19ad75044206b408e7b7e1a353578e0fb741131b

Transactions (1)

Coinbase6a703d83e5cfca…578e0fb741131b

1 in → 42 out10.0500 XPM1.46 KB

ARXSrG7z…CRW69WR4 ANuKx9Ke…wm7nrBRq ANo4YY1x…vnsPRDSU Acs9SHrk…QJSB8SFG APVGazMT…cDCk2nwA

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.

2.824 × 10⁹³(94-digit number)

28249711372684242292…44268264949194371561

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

2.824 × 10⁹³(94-digit number)

28249711372684242292…44268264949194371561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.649 × 10⁹³(94-digit number)

56499422745368484585…88536529898388743121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.129 × 10⁹⁴(95-digit number)

11299884549073696917…77073059796777486241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.259 × 10⁹⁴(95-digit number)

22599769098147393834…54146119593554972481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.519 × 10⁹⁴(95-digit number)

45199538196294787668…08292239187109944961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.039 × 10⁹⁴(95-digit number)

90399076392589575336…16584478374219889921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.807 × 10⁹⁵(96-digit number)

18079815278517915067…33168956748439779841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.615 × 10⁹⁵(96-digit number)

36159630557035830134…66337913496879559681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.231 × 10⁹⁵(96-digit number)

72319261114071660269…32675826993759119361

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

Block #241,190

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