Block #504,360

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/21/2014, 5:48:12 PM · Difficulty 10.8087 · 6,299,239 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5f2ef80baf9865823fef9dff5bf4671503a9e82bcb8712df04528f5f2d11d5d1

View on Chainz ↗

Height

#504,360

Difficulty

10.808701

Transactions

Size

800 B

Version

Bits

0acf070b

Nonce

351,212,963

Timestamp

4/21/2014, 5:48:12 PM

Confirmations

6,299,239

Mined by

⛏️ aSUYAREQGaCCeRHuaNkf53p3iT4PbrV47D9Shh

Merkle Root

34b7b11dc8b49a8dd2e0c9aee6d48abf20a944955e1176b5160f62b404276280

Transactions (1)

Coinbase34b7b11dc8b49a…0f62b404276280

1 in → 19 out8.5500 XPM709 B

AREQGaCC…V47D9Shh AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 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.

9.048 × 10⁹⁷(98-digit number)

90481869027459579747…79811070068668853759

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

9.048 × 10⁹⁷(98-digit number)

90481869027459579747…79811070068668853759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.809 × 10⁹⁸(99-digit number)

18096373805491915949…59622140137337707519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.619 × 10⁹⁸(99-digit number)

36192747610983831899…19244280274675415039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.238 × 10⁹⁸(99-digit number)

72385495221967663798…38488560549350830079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.447 × 10⁹⁹(100-digit number)

14477099044393532759…76977121098701660159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.895 × 10⁹⁹(100-digit number)

28954198088787065519…53954242197403320319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.790 × 10⁹⁹(100-digit number)

57908396177574131038…07908484394806640639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.158 × 10¹⁰⁰(101-digit number)

11581679235514826207…15816968789613281279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.316 × 10¹⁰⁰(101-digit number)

23163358471029652415…31633937579226562559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.632 × 10¹⁰⁰(101-digit number)

46326716942059304830…63267875158453125119

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