Block #494,700

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/16/2014, 7:15:46 AM · Difficulty 10.7236 · 6,313,477 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

ec2429b83ada4bfba2f3474a6cdd390142bf56fb1eeeb78c5733a6904b9ad295

View on Chainz ↗

Height

#494,700

Difficulty

10.723564

Transactions

Size

798 B

Version

Bits

0ab93b76

Nonce

354,285

Timestamp

4/16/2014, 7:15:46 AM

Confirmations

6,313,477

Mined by

⛏️ laSN-AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

b45c9d84606f32eb265d6d3ff26fb48783cc226c87529c2f4349d580e7466473

Transactions (1)

Coinbaseb45c9d84606f32…49d580e7466473

1 in → 19 out8.6800 XPM709 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 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.

3.074 × 10⁹²(93-digit number)

30746741871520177765…32533385882001475199

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

3.074 × 10⁹²(93-digit number)

30746741871520177765…32533385882001475199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.149 × 10⁹²(93-digit number)

61493483743040355531…65066771764002950399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.229 × 10⁹³(94-digit number)

12298696748608071106…30133543528005900799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.459 × 10⁹³(94-digit number)

24597393497216142212…60267087056011801599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.919 × 10⁹³(94-digit number)

49194786994432284425…20534174112023603199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.838 × 10⁹³(94-digit number)

98389573988864568850…41068348224047206399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.967 × 10⁹⁴(95-digit number)

19677914797772913770…82136696448094412799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.935 × 10⁹⁴(95-digit number)

39355829595545827540…64273392896188825599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.871 × 10⁹⁴(95-digit number)

78711659191091655080…28546785792377651199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.574 × 10⁹⁵(96-digit number)

15742331838218331016…57093571584755302399

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 #494,700

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