Block #365,392

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/18/2014, 5:27:38 PM · Difficulty 10.4246 · 6,430,769 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e1caea14f99d765230d01a7fa24c6102b61258dd83c72cfaf3104793d88b4816

View on Chainz ↗

Height

#365,392

Difficulty

10.424646

Transactions

Size

1002 B

Version

Bits

0a6cb5a1

Nonce

24,754

Timestamp

1/18/2014, 5:27:38 PM

Confirmations

6,430,769

Mined by

⛏️ PaRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

47a5afa7fde1a92aeb818f5c2fb990dfa3091e04b8c10853947ce64bdea40b03

Transactions (1)

Coinbase47a5afa7fde1a9…7ce64bdea40b03

1 in → 25 out9.1900 XPM912 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz

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.

2.884 × 10⁹⁵(96-digit number)

28847414300195067085…27879316775959436601

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

2.884 × 10⁹⁵(96-digit number)

28847414300195067085…27879316775959436601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.769 × 10⁹⁵(96-digit number)

57694828600390134171…55758633551918873201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.153 × 10⁹⁶(97-digit number)

11538965720078026834…11517267103837746401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.307 × 10⁹⁶(97-digit number)

23077931440156053668…23034534207675492801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.615 × 10⁹⁶(97-digit number)

46155862880312107337…46069068415350985601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.231 × 10⁹⁶(97-digit number)

92311725760624214674…92138136830701971201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.846 × 10⁹⁷(98-digit number)

18462345152124842934…84276273661403942401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.692 × 10⁹⁷(98-digit number)

36924690304249685869…68552547322807884801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.384 × 10⁹⁷(98-digit number)

73849380608499371739…37105094645615769601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.476 × 10⁹⁸(99-digit number)

14769876121699874347…74210189291231539201

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