Block #256,976

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/12/2013, 4:42:10 AM · Difficulty 9.9754 · 6,546,816 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

648feb5fa8edd7768881130752904f6f4e7f5e0384df5d7a3c5244ddd2599305

View on Chainz ↗

Height

#256,976

Difficulty

9.975387

Transactions

Size

1.54 KB

Version

Bits

09f9b2ee

Nonce

28,861

Timestamp

11/12/2013, 4:42:10 AM

Confirmations

6,546,816

Mined by

⛏️ aRAZCxh8KcCGpmezBtRzLeprqWKYdm73BrBd

Merkle Root

4ef4f96e0469cb9aa1efcae0d21ee453ebb9e905fe2acdac43d309fe27b26e4d

Transactions (1)

Coinbase4ef4f96e0469cb…d309fe27b26e4d

1 in → 42 out10.0099 XPM1.46 KB

AZCxh8Kc…dm73BrBd AabHNb1B…GRoingRy AQtzUSwq…htAuF3yC ARR7aRH6…ne3DXGXZ AKDTDDtx…iqvw9cdY

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.

3.531 × 10⁹⁴(95-digit number)

35317954164562619082…19328002633594994959

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

3.531 × 10⁹⁴(95-digit number)

35317954164562619082…19328002633594994959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.063 × 10⁹⁴(95-digit number)

70635908329125238165…38656005267189989919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.412 × 10⁹⁵(96-digit number)

14127181665825047633…77312010534379979839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.825 × 10⁹⁵(96-digit number)

28254363331650095266…54624021068759959679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.650 × 10⁹⁵(96-digit number)

56508726663300190532…09248042137519919359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.130 × 10⁹⁶(97-digit number)

11301745332660038106…18496084275039838719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.260 × 10⁹⁶(97-digit number)

22603490665320076212…36992168550079677439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.520 × 10⁹⁶(97-digit number)

45206981330640152425…73984337100159354879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.041 × 10⁹⁶(97-digit number)

90413962661280304851…47968674200318709759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.808 × 10⁹⁷(98-digit number)

18082792532256060970…95937348400637419519

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer