Block #281,792

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/29/2013, 3:55:10 AM · Difficulty 9.9777 · 6,513,782 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ae8ddcf3863e667e255ae70f41417a7aac59c323bb7400a8a267ffc0f8bd61ba

View on Chainz ↗

Height

#281,792

Difficulty

9.977726

Transactions

Size

1.11 KB

Version

Bits

09fa4c48

Nonce

14,547

Timestamp

11/29/2013, 3:55:10 AM

Confirmations

6,513,782

Mined by

⛏️ LaRAWJ9D7ctTXD2TwswcccwNBFLZCafienv32

Merkle Root

ed88b8620187cd41378b34702d9159c0d4ee4db24a66b13ca9d9f83dfa08e0fc

Transactions (1)

Coinbaseed88b8620187cd…d9f83dfa08e0fc

1 in → 29 out10.0100 XPM1.02 KB

AWJ9D7ct…afienv32 ALw8WzMm…sj2uYfgL AGFAJ5YL…ZEnBbk6G ALUWNKdQ…8E5fDZ7s APFsQ3Fo…xoFKrF12

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.

2.428 × 10⁹⁴(95-digit number)

24288497698699218608…76648107188729884161

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

2.428 × 10⁹⁴(95-digit number)

24288497698699218608…76648107188729884161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.857 × 10⁹⁴(95-digit number)

48576995397398437216…53296214377459768321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.715 × 10⁹⁴(95-digit number)

97153990794796874433…06592428754919536641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.943 × 10⁹⁵(96-digit number)

19430798158959374886…13184857509839073281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.886 × 10⁹⁵(96-digit number)

38861596317918749773…26369715019678146561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.772 × 10⁹⁵(96-digit number)

77723192635837499546…52739430039356293121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.554 × 10⁹⁶(97-digit number)

15544638527167499909…05478860078712586241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.108 × 10⁹⁶(97-digit number)

31089277054334999818…10957720157425172481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.217 × 10⁹⁶(97-digit number)

62178554108669999637…21915440314850344961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.243 × 10⁹⁷(98-digit number)

12435710821733999927…43830880629700689921

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