Block #290,089

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/2/2013, 12:44:46 PM · Difficulty 9.9890 · 6,505,338 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e6c00483a495840e7e7ef56afb04b81f03c51b3f2294519467b77e3e50499160

View on Chainz ↗

Height

#290,089

Difficulty

9.988984

Transactions

Size

1.11 KB

Version

Bits

09fd2e11

Nonce

32,701

Timestamp

12/2/2013, 12:44:46 PM

Confirmations

6,505,338

Mined by

⛏️ maRZAKde1i4dpqpgDtEArAY3oRXX8K88R1bw6g

Merkle Root

2b1d9c815a95ec3aff5c953e751c9d3649d936b6a8bddabf986d88db5d65245a

Transactions (1)

Coinbase2b1d9c815a95ec…6d88db5d65245a

1 in → 29 out9.9900 XPM1.02 KB

AKde1i4d…88R1bw6g AWA5FEzr…x9RdPKTy AdwTEXyC…NwbVbqZV AXLJzdRc…LJLLZDBD AXz2kWvX…V5ZFCDBd

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.

3.746 × 10⁹¹(92-digit number)

37464300576405145532…10759836760071098561

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

3.746 × 10⁹¹(92-digit number)

37464300576405145532…10759836760071098561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.492 × 10⁹¹(92-digit number)

74928601152810291064…21519673520142197121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.498 × 10⁹²(93-digit number)

14985720230562058212…43039347040284394241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.997 × 10⁹²(93-digit number)

29971440461124116425…86078694080568788481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.994 × 10⁹²(93-digit number)

59942880922248232851…72157388161137576961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.198 × 10⁹³(94-digit number)

11988576184449646570…44314776322275153921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.397 × 10⁹³(94-digit number)

23977152368899293140…88629552644550307841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.795 × 10⁹³(94-digit number)

47954304737798586281…77259105289100615681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

9.590 × 10⁹³(94-digit number)

95908609475597172562…54518210578201231361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.918 × 10⁹⁴(95-digit number)

19181721895119434512…09036421156402462721

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