Block #494,687

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/16/2014, 7:02:44 AM · Difficulty 10.7235 · 6,296,775 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5f3e6e28bf68fcf399462af78f7e9b95066d63ed634badb7d37c62b2a976ad6a

View on Chainz ↗

Height

#494,687

Difficulty

10.723545

Transactions

Size

868 B

Version

Bits

0ab93a39

Nonce

7,242

Timestamp

4/16/2014, 7:02:44 AM

Confirmations

6,296,775

Merkle Root

f053af8e29ad925523a7e5d6d5183a6667c4dfb66e1e9621da0c5199e9a7f730

Transactions (1)

Coinbasef053af8e29ad92…0c5199e9a7f730

1 in → 21 out8.6800 XPM776 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AQ8QAT3J…rCFKuVbR AWMrD5hP…ZwsoxvZ3

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.

2.402 × 10⁹⁹(100-digit number)

24027197053999780894…12237258533780149759

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

2.402 × 10⁹⁹(100-digit number)

24027197053999780894…12237258533780149759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.805 × 10⁹⁹(100-digit number)

48054394107999561788…24474517067560299519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.610 × 10⁹⁹(100-digit number)

96108788215999123577…48949034135120599039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.922 × 10¹⁰⁰(101-digit number)

19221757643199824715…97898068270241198079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.844 × 10¹⁰⁰(101-digit number)

38443515286399649431…95796136540482396159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.688 × 10¹⁰⁰(101-digit number)

76887030572799298862…91592273080964792319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.537 × 10¹⁰¹(102-digit number)

15377406114559859772…83184546161929584639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.075 × 10¹⁰¹(102-digit number)

30754812229119719544…66369092323859169279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.150 × 10¹⁰¹(102-digit number)

61509624458239439089…32738184647718338559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.230 × 10¹⁰²(103-digit number)

12301924891647887817…65476369295436677119

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