Block #200,833

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/9/2013, 6:27:43 AM · Difficulty 9.8904 · 6,598,616 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d4f1dd2e81e874a326a9f4ce5fcc634b039243ba8a8a5f572167f9f4712f4035

View on Chainz ↗

Height

#200,833

Difficulty

9.890367

Transactions

Size

4.70 KB

Version

Bits

09e3ef11

Nonce

1,165,039,871

Timestamp

10/9/2013, 6:27:43 AM

Confirmations

6,598,616

Mined by

⛏️ RTAczTyhoVYRURtoABJBwyUe7gRnBMxvtszB

Merkle Root

459e5e8a00fd37692c472b7c80418817d3c70540926ba8e1f94736baf3da3164

Transactions (1)

Coinbase459e5e8a00fd37…4736baf3da3164

1 in → 137 out10.1600 XPM4.61 KB

AczTyhoV…BMxvtszB AWWaDRnP…qR1zB7PV AULkeUhX…SqqohfrX AdwTEXyC…NwbVbqZV AeMCTwXK…dtV9dA72

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.

7.797 × 10⁸⁸(89-digit number)

77976539183054090395…15760029286421155081

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

7.797 × 10⁸⁸(89-digit number)

77976539183054090395…15760029286421155081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.559 × 10⁸⁹(90-digit number)

15595307836610818079…31520058572842310161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.119 × 10⁸⁹(90-digit number)

31190615673221636158…63040117145684620321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.238 × 10⁸⁹(90-digit number)

62381231346443272316…26080234291369240641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.247 × 10⁹⁰(91-digit number)

12476246269288654463…52160468582738481281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.495 × 10⁹⁰(91-digit number)

24952492538577308926…04320937165476962561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.990 × 10⁹⁰(91-digit number)

49904985077154617853…08641874330953925121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.980 × 10⁹⁰(91-digit number)

99809970154309235706…17283748661907850241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.996 × 10⁹¹(92-digit number)

19961994030861847141…34567497323815700481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.992 × 10⁹¹(92-digit number)

39923988061723694282…69134994647631400961

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