Block #50,963

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/16/2013, 3:45:21 AM · Difficulty 8.8911 · 6,738,984 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

09fdec5310865b406a74f68c82b1117fb4d7277dc013ccedd1d8545e1065e9f7

View on Chainz ↗

Height

#50,963

Difficulty

8.891055

Transactions

Size

199 B

Version

Bits

08e41c30

Nonce

2,140

Timestamp

7/16/2013, 3:45:21 AM

Confirmations

6,738,984

Merkle Root

39787531694216b71ad1b798370740e18d297b79a55980b71fc7e95f7f023c9d

Transactions (1)

Coinbase39787531694216…c7e95f7f023c9d

1 in → 1 out12.6300 XPM110 B

AeTcmmqH…LrFchfe1

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.

2.222 × 10⁹³(94-digit number)

22229401918934757279…94825621722737585041

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

2.222 × 10⁹³(94-digit number)

22229401918934757279…94825621722737585041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.445 × 10⁹³(94-digit number)

44458803837869514559…89651243445475170081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.891 × 10⁹³(94-digit number)

88917607675739029118…79302486890950340161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.778 × 10⁹⁴(95-digit number)

17783521535147805823…58604973781900680321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.556 × 10⁹⁴(95-digit number)

35567043070295611647…17209947563801360641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.113 × 10⁹⁴(95-digit number)

71134086140591223294…34419895127602721281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.422 × 10⁹⁵(96-digit number)

14226817228118244658…68839790255205442561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.845 × 10⁹⁵(96-digit number)

28453634456236489317…37679580510410885121

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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