Block #794,492

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/2/2014, 10:49:13 PM · Difficulty 10.9750 · 5,997,736 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2e94aede03203eaf343efb8e4febf27e1e522ad17e319a0177624456883f3635

View on Chainz ↗

Height

#794,492

Difficulty

10.974960

Transactions

Size

434 B

Version

Bits

0af996f9

Nonce

247,764,738

Timestamp

11/2/2014, 10:49:13 PM

Confirmations

5,997,736

Merkle Root

0abca2b371bcacd85e4ec1359de093d9714d0091164ce696db596fffb7871e41

Transactions (2)

Coinbase1d2c66a8036e9a…640a8f75cdc2a9

1 in → 1 out8.3000 XPM116 B

ANSXnLY2…Sd25TjkD

029a627f8335f3…42aadbe4a52814

1 in → 2 out0.5546 XPM226 B

AGXqJki6…YNiMZGMN AN9GQ3WU…ZfSNSRnF

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.

3.854 × 10⁹⁸(99-digit number)

38543833132945754646…55357360379118694401

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

3.854 × 10⁹⁸(99-digit number)

38543833132945754646…55357360379118694401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.708 × 10⁹⁸(99-digit number)

77087666265891509292…10714720758237388801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.541 × 10⁹⁹(100-digit number)

15417533253178301858…21429441516474777601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.083 × 10⁹⁹(100-digit number)

30835066506356603717…42858883032949555201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.167 × 10⁹⁹(100-digit number)

61670133012713207434…85717766065899110401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.233 × 10¹⁰⁰(101-digit number)

12334026602542641486…71435532131798220801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.466 × 10¹⁰⁰(101-digit number)

24668053205085282973…42871064263596441601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.933 × 10¹⁰⁰(101-digit number)

49336106410170565947…85742128527192883201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

9.867 × 10¹⁰⁰(101-digit number)

98672212820341131894…71484257054385766401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.973 × 10¹⁰¹(102-digit number)

19734442564068226378…42968514108771532801

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