Block #393,643

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/7/2014, 7:52:24 AM · Difficulty 10.4357 · 6,415,953 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ff35e593bb4a44218156f7581c3d91c7af0652ba21168be88cda9847ee6c8617

View on Chainz ↗

Height

#393,643

Difficulty

10.435656

Transactions

Size

935 B

Version

Bits

0a6f8723

Nonce

9,368

Timestamp

2/7/2014, 7:52:24 AM

Confirmations

6,415,953

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

f1ce303a5df84cbeb2ffda40f765d2d8c5f2a665168250aa817f3b3e4ac5318a

Transactions (1)

Coinbasef1ce303a5df84c…7f3b3e4ac5318a

1 in → 23 out9.1700 XPM845 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AZV4TwxQ…8JnQqSoH

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.

7.495 × 10⁹⁵(96-digit number)

74958920864547490629…44391659691139517439

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

7.495 × 10⁹⁵(96-digit number)

74958920864547490629…44391659691139517439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.499 × 10⁹⁶(97-digit number)

14991784172909498125…88783319382279034879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.998 × 10⁹⁶(97-digit number)

29983568345818996251…77566638764558069759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.996 × 10⁹⁶(97-digit number)

59967136691637992503…55133277529116139519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.199 × 10⁹⁷(98-digit number)

11993427338327598500…10266555058232279039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.398 × 10⁹⁷(98-digit number)

23986854676655197001…20533110116464558079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.797 × 10⁹⁷(98-digit number)

47973709353310394002…41066220232929116159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.594 × 10⁹⁷(98-digit number)

95947418706620788005…82132440465858232319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.918 × 10⁹⁸(99-digit number)

19189483741324157601…64264880931716464639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.837 × 10⁹⁸(99-digit number)

38378967482648315202…28529761863432929279

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

Block #393,643

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