Block #504,533

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/21/2014, 8:19:23 PM · Difficulty 10.8096 · 6,299,266 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5c1c37ae71a44d36191b25ecf7a0b19d99cd9b837a621cd1678df4db5028636a

View on Chainz ↗

Height

#504,533

Difficulty

10.809562

Transactions

Size

799 B

Version

Bits

0acf3f6e

Nonce

945

Timestamp

4/21/2014, 8:19:23 PM

Confirmations

6,299,266

Mined by

⛏️ aSU}AREQGaCCeRHuaNkf53p3iT4PbrV47D9Shh

Merkle Root

957e21f175c6d1dfaa0930d1c07b05c7c1506cf382eb36de51a14b0a5ef8802f

Transactions (1)

Coinbase957e21f175c6d1…a14b0a5ef8802f

1 in → 19 out8.5400 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.

1.517 × 10⁹⁵(96-digit number)

15174909633698644799…05097272507521091839

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

1.517 × 10⁹⁵(96-digit number)

15174909633698644799…05097272507521091839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.034 × 10⁹⁵(96-digit number)

30349819267397289599…10194545015042183679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.069 × 10⁹⁵(96-digit number)

60699638534794579198…20389090030084367359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.213 × 10⁹⁶(97-digit number)

12139927706958915839…40778180060168734719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.427 × 10⁹⁶(97-digit number)

24279855413917831679…81556360120337469439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.855 × 10⁹⁶(97-digit number)

48559710827835663359…63112720240674938879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.711 × 10⁹⁶(97-digit number)

97119421655671326718…26225440481349877759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.942 × 10⁹⁷(98-digit number)

19423884331134265343…52450880962699755519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.884 × 10⁹⁷(98-digit number)

38847768662268530687…04901761925399511039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.769 × 10⁹⁷(98-digit number)

77695537324537061374…09803523850799022079

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