Block #521,097

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/2/2014, 6:43:47 AM · Difficulty 10.8607 · 6,289,953 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f4452129579238b761d2c480783616ccc7d9c2f64dd9d19b6c84915677dd8f74

View on Chainz ↗

Height

#521,097

Difficulty

10.860652

Transactions

Size

697 B

Version

Bits

0adc53ab

Nonce

405,087

Timestamp

5/2/2014, 6:43:47 AM

Confirmations

6,289,953

Mined by

⛏️ aSc>F"AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

427d717734a009055784af94f427f674fa8d59e71c9e83714e76e455e435d234

Transactions (1)

Coinbase427d717734a009…76e455e435d234

1 in → 16 out8.4600 XPM607 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q AJtNW28X…Syb4Ph5j

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.

1.454 × 10⁹⁴(95-digit number)

14540687110880660609…31513682931108948479

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

1.454 × 10⁹⁴(95-digit number)

14540687110880660609…31513682931108948479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.908 × 10⁹⁴(95-digit number)

29081374221761321218…63027365862217896959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.816 × 10⁹⁴(95-digit number)

58162748443522642436…26054731724435793919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.163 × 10⁹⁵(96-digit number)

11632549688704528487…52109463448871587839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.326 × 10⁹⁵(96-digit number)

23265099377409056974…04218926897743175679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.653 × 10⁹⁵(96-digit number)

46530198754818113949…08437853795486351359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.306 × 10⁹⁵(96-digit number)

93060397509636227898…16875707590972702719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.861 × 10⁹⁶(97-digit number)

18612079501927245579…33751415181945405439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.722 × 10⁹⁶(97-digit number)

37224159003854491159…67502830363890810879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.444 × 10⁹⁶(97-digit number)

74448318007708982318…35005660727781621759

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 #521,097

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