Block #250,396

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/8/2013, 11:44:13 AM · Difficulty 9.9683 · 6,545,165 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a1e86264871ee4b8b42612b1764928333f081dc3b31c1944a016a144967cb837

View on Chainz ↗

Height

#250,396

Difficulty

9.968262

Transactions

Size

4.56 KB

Version

Bits

09f7e006

Nonce

4,084

Timestamp

11/8/2013, 11:44:13 AM

Confirmations

6,545,165

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

0996e986edd0d1265d6e870ca84a9343744705ddc0e607a166cf973503d9867c

Transactions (2)

Coinbase50a0ffc63eb2b4…02838f1263c91c

1 in → 2 out10.1000 XPM136 B

AZDUEbdS…RYKMRZET AU6kq4CL…dQBLvxLp

3a34c4bf0c142d…f725efe075151a

38 in → 2 out373.7366 XPM4.34 KB

AR24vtgA…DNdtqa6z AMa2WoKe…RgX4EdWb

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.

1.254 × 10⁹⁵(96-digit number)

12548300022383820307…96805555858623133041

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

1.254 × 10⁹⁵(96-digit number)

12548300022383820307…96805555858623133041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.509 × 10⁹⁵(96-digit number)

25096600044767640614…93611111717246266081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.019 × 10⁹⁵(96-digit number)

50193200089535281229…87222223434492532161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.003 × 10⁹⁶(97-digit number)

10038640017907056245…74444446868985064321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.007 × 10⁹⁶(97-digit number)

20077280035814112491…48888893737970128641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.015 × 10⁹⁶(97-digit number)

40154560071628224983…97777787475940257281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.030 × 10⁹⁶(97-digit number)

80309120143256449967…95555574951880514561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.606 × 10⁹⁷(98-digit number)

16061824028651289993…91111149903761029121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.212 × 10⁹⁷(98-digit number)

32123648057302579987…82222299807522058241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.424 × 10⁹⁷(98-digit number)

64247296114605159974…64444599615044116481

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