Block #222,763

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/22/2013, 11:13:17 AM · Difficulty 9.9389 · 6,582,400 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7f874468e334b365431b42f2384be31b243749879e9023a0fe75ddd0d4a24f2a

View on Chainz ↗

Height

#222,763

Difficulty

9.938864

Transactions

Size

1.48 KB

Version

Bits

09f05966

Nonce

25,514

Timestamp

10/22/2013, 11:13:17 AM

Confirmations

6,582,400

Mined by

⛏️ +fRfAMV2CWW7tYmWaAy1tEgYhePZNiyebsFBrS

Merkle Root

04928bf4491d65a315b95d954af11c40e0ece6bd4356e40fef6c45eb2629d684

Transactions (1)

Coinbase04928bf4491d65…6c45eb2629d684

1 in → 40 out10.0900 XPM1.39 KB

AMV2CWW7…yebsFBrS AeZmMFY8…mjAy5Mi4 AKXeSXzu…yeuNjvhB ARpndEmc…Hg792kEk APw6W8tk…RgVVbThY

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.

3.312 × 10⁹²(93-digit number)

33129750053458869360…24257750370743296721

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

3.312 × 10⁹²(93-digit number)

33129750053458869360…24257750370743296721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.625 × 10⁹²(93-digit number)

66259500106917738720…48515500741486593441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.325 × 10⁹³(94-digit number)

13251900021383547744…97031001482973186881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.650 × 10⁹³(94-digit number)

26503800042767095488…94062002965946373761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.300 × 10⁹³(94-digit number)

53007600085534190976…88124005931892747521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.060 × 10⁹⁴(95-digit number)

10601520017106838195…76248011863785495041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.120 × 10⁹⁴(95-digit number)

21203040034213676390…52496023727570990081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.240 × 10⁹⁴(95-digit number)

42406080068427352781…04992047455141980161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.481 × 10⁹⁴(95-digit number)

84812160136854705562…09984094910283960321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.696 × 10⁹⁵(96-digit number)

16962432027370941112…19968189820567920641

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