Block #246,217

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/5/2013, 11:25:40 PM · Difficulty 9.9643 · 6,557,415 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

296af194850d3fb3a848867f43348f781390d36d54efa9a47f8f7a148d1591bb

View on Chainz ↗

Height

#246,217

Difficulty

9.964346

Transactions

Size

1.91 KB

Version

Bits

09f6df5c

Nonce

14,103

Timestamp

11/5/2013, 11:25:40 PM

Confirmations

6,557,415

Mined by

⛏️ Ry~UAZrPRT4s5yBYR2s1LYT4ykioPiPz2AcjLi

Merkle Root

0897656607f4e7d3e265e73d8ce306bc8ef490d85e5d7899a4b5a1d6f59afe24

Transactions (1)

Coinbase0897656607f4e7…b5a1d6f59afe24

1 in → 53 out10.0400 XPM1.82 KB

AZrPRT4s…Pz2AcjLi AdnG9gQ7…N9B7mA2p AQtzUSwq…htAuF3yC AMttQDuf…7j6tfS9x AMbCuLHZ…WSoStwkc

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.

2.831 × 10⁹⁴(95-digit number)

28316433753685671332…73365099630682206401

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

2.831 × 10⁹⁴(95-digit number)

28316433753685671332…73365099630682206401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.663 × 10⁹⁴(95-digit number)

56632867507371342665…46730199261364412801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.132 × 10⁹⁵(96-digit number)

11326573501474268533…93460398522728825601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.265 × 10⁹⁵(96-digit number)

22653147002948537066…86920797045457651201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.530 × 10⁹⁵(96-digit number)

45306294005897074132…73841594090915302401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.061 × 10⁹⁵(96-digit number)

90612588011794148264…47683188181830604801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.812 × 10⁹⁶(97-digit number)

18122517602358829652…95366376363661209601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.624 × 10⁹⁶(97-digit number)

36245035204717659305…90732752727322419201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.249 × 10⁹⁶(97-digit number)

72490070409435318611…81465505454644838401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.449 × 10⁹⁷(98-digit number)

14498014081887063722…62931010909289676801

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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