Block #268,695

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/22/2013, 8:21:58 AM · Difficulty 9.9568 · 6,547,524 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7839918ac07d6c1e9e19fd275d098603478275c2512adc65f78ec7b96f20e345

View on Chainz ↗

Height

#268,695

Difficulty

9.956824

Transactions

Size

1.87 KB

Version

Bits

09f4f26b

Nonce

53,787

Timestamp

11/22/2013, 8:21:58 AM

Confirmations

6,547,524

Mined by

⛏️ aR{AeLjc3taqj48BJZKRddRpUKxx76Gk5xuJk

Merkle Root

0fad53f835f402b247d32b3b62a9d0e6af8186e3e7af0636297094ab99529a53

Transactions (1)

Coinbase0fad53f835f402…7094ab99529a53

1 in → 52 out10.0500 XPM1.79 KB

AeLjc3ta…6Gk5xuJk AThYr9m5…KGSuN7FQ APfbVzNM…GWk2KPXG ARpndEmc…Hg792kEk APZy8y6E…QZaGQjfp

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.

3.983 × 10⁸⁸(89-digit number)

39836316760432216388…77498026277970750751

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

3.983 × 10⁸⁸(89-digit number)

39836316760432216388…77498026277970750751

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.967 × 10⁸⁸(89-digit number)

79672633520864432776…54996052555941501501

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.593 × 10⁸⁹(90-digit number)

15934526704172886555…09992105111883003001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.186 × 10⁸⁹(90-digit number)

31869053408345773110…19984210223766006001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.373 × 10⁸⁹(90-digit number)

63738106816691546220…39968420447532012001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.274 × 10⁹⁰(91-digit number)

12747621363338309244…79936840895064024001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.549 × 10⁹⁰(91-digit number)

25495242726676618488…59873681790128048001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.099 × 10⁹⁰(91-digit number)

50990485453353236976…19747363580256096001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.019 × 10⁹¹(92-digit number)

10198097090670647395…39494727160512192001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.039 × 10⁹¹(92-digit number)

20396194181341294790…78989454321024384001

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 #268,695

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