Block #291,593

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/3/2013, 6:46:06 AM · Difficulty 9.9899 · 6,513,814 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4ef93867dccca0200231ea219c1b897ff91596453cad5c9b75d0a658358fe326

View on Chainz ↗

Height

#291,593

Difficulty

9.989915

Transactions

Size

1.01 KB

Version

Bits

09fd6b14

Nonce

234,445

Timestamp

12/3/2013, 6:46:06 AM

Confirmations

6,513,814

Mined by

⛏️ saR~ARzXge7STrHg8ZTMRW57MCNAWRCEjL5oYm

Merkle Root

a2608f2fd2c4d069b8fcfc9d0b44a7b6cfa82ef0460d0c39d7b085072c9121e7

Transactions (1)

Coinbasea2608f2fd2c4d0…b085072c9121e7

1 in → 26 out10.0100 XPM947 B

ARzXge7S…CEjL5oYm AYcLTeXR…bscgPops AWm233nS…1dJSnVJJ ASdFbQ41…WNAgRmiJ AdCkmCQc…L4UdmY7c

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.

1.167 × 10⁹⁴(95-digit number)

11676061574221190352…55228011985936924761

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

1.167 × 10⁹⁴(95-digit number)

11676061574221190352…55228011985936924761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.335 × 10⁹⁴(95-digit number)

23352123148442380705…10456023971873849521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.670 × 10⁹⁴(95-digit number)

46704246296884761411…20912047943747699041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.340 × 10⁹⁴(95-digit number)

93408492593769522822…41824095887495398081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.868 × 10⁹⁵(96-digit number)

18681698518753904564…83648191774990796161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.736 × 10⁹⁵(96-digit number)

37363397037507809129…67296383549981592321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.472 × 10⁹⁵(96-digit number)

74726794075015618258…34592767099963184641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.494 × 10⁹⁶(97-digit number)

14945358815003123651…69185534199926369281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.989 × 10⁹⁶(97-digit number)

29890717630006247303…38371068399852738561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.978 × 10⁹⁶(97-digit number)

59781435260012494606…76742136799705477121

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