Block #250,033

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/8/2013, 7:24:00 AM · Difficulty 9.9676 · 6,589,342 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

6862f3904a6158fe3826434c480f9d37e4963de46cf65b453869c3693f41ce6e

View on Chainz ↗

Height

#250,033

Difficulty

9.967606

Transactions

Size

2.11 KB

Version

Bits

09f7b50c

Nonce

428,207

Timestamp

11/8/2013, 7:24:00 AM

Confirmations

6,589,342

Mined by

⛏️ aR|APHngwz27GMW45jJC6wSAHExgSoXWG6CFr

Merkle Root

70a3cd52007df85ec3d8a20ae85f4830df12c93951f67ee77390b893ea4654ef

Transactions (1)

Coinbase70a3cd52007df8…90b893ea4654ef

1 in → 59 out10.0170 XPM2.02 KB

APHngwz2…oXWG6CFr ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC ALzxhR4e…bD4bNcZe ALd5yTY2…vgfAFVPZ

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.

7.967 × 10⁸⁸(89-digit number)

79671890919246307766…12328064235362330611

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

7.967 × 10⁸⁸(89-digit number)

79671890919246307766…12328064235362330611

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.593 × 10⁸⁹(90-digit number)

15934378183849261553…24656128470724661221

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.186 × 10⁸⁹(90-digit number)

31868756367698523106…49312256941449322441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.373 × 10⁸⁹(90-digit number)

63737512735397046213…98624513882898644881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.274 × 10⁹⁰(91-digit number)

12747502547079409242…97249027765797289761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.549 × 10⁹⁰(91-digit number)

25495005094158818485…94498055531594579521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.099 × 10⁹⁰(91-digit number)

50990010188317636970…88996111063189159041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.019 × 10⁹¹(92-digit number)

10198002037663527394…77992222126378318081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.039 × 10⁹¹(92-digit number)

20396004075327054788…55984444252756636161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.079 × 10⁹¹(92-digit number)

40792008150654109576…11968888505513272321

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

Block #250,033

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