Block #291,843

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/3/2013, 9:54:26 AM · Difficulty 9.9900 · 6,511,080 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

728666b511bcd152680bb23f8bc7c0fb06eae903ec124153877b74b241a9b188

View on Chainz ↗

Height

#291,843

Difficulty

9.990047

Transactions

Size

1.04 KB

Version

Bits

09fd73b2

Nonce

106,397

Timestamp

12/3/2013, 9:54:26 AM

Confirmations

6,511,080

Mined by

⛏️ taR'AZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

ee53161e24c882e09137d785a7c22be18f57aeedfd443dc26b8c51b5980ccacc

Transactions (1)

Coinbaseee53161e24c882…8c51b5980ccacc

1 in → 27 out10.0000 XPM981 B

AZninDSu…FvgDMwC4 APFsQ3Fo…xoFKrF12 Ad9pSzHt…cpJ3y2zz ASXEwJrb…E3MLWChF AZ2pPuKg…95SN2Yr7

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.

4.126 × 10⁹²(93-digit number)

41260737772867596274…92350732619905070951

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

4.126 × 10⁹²(93-digit number)

41260737772867596274…92350732619905070951

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.252 × 10⁹²(93-digit number)

82521475545735192548…84701465239810141901

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.650 × 10⁹³(94-digit number)

16504295109147038509…69402930479620283801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.300 × 10⁹³(94-digit number)

33008590218294077019…38805860959240567601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.601 × 10⁹³(94-digit number)

66017180436588154038…77611721918481135201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.320 × 10⁹⁴(95-digit number)

13203436087317630807…55223443836962270401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.640 × 10⁹⁴(95-digit number)

26406872174635261615…10446887673924540801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.281 × 10⁹⁴(95-digit number)

52813744349270523230…20893775347849081601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.056 × 10⁹⁵(96-digit number)

10562748869854104646…41787550695698163201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.112 × 10⁹⁵(96-digit number)

21125497739708209292…83575101391396326401

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