Block #30,180

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/13/2013, 6:09:38 PM · Difficulty 7.9863 · 6,765,313 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

5d5bd54785cd8b5107434bb2bec1e936433f2ae39a363195c68b0ca1cf1b0a5f

View on Chainz ↗

Height

#30,180

Difficulty

7.986329

Transactions

Size

748 B

Version

Bits

07fc8014

Nonce

Timestamp

7/13/2013, 6:09:38 PM

Confirmations

6,765,313

Mined by

⛏️ P2SHAVyqrBofadUQCQ9TJWV2x3kdvgzv2xZAg6

Merkle Root

d9ad9e0bb719b211c6ecad760036ddff093d88f3626ec5d2ee66f8a65f359995

Transactions (3)

Coinbase666bec425f7557…41b766443d683a

1 in → 1 out15.6800 XPM108 B

AVyqrBof…zv2xZAg6

f029e5fda9c637…f73bfd55ec21fd

2 in → 1 out33.8300 XPM272 B

AaNMrVuB…vz8xMmHF

76364ccdd9aa0b…1b2ea8d13f477f

2 in → 1 out31.4200 XPM274 B

Ab6XQdqw…TCF9niBG

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.

6.314 × 10¹⁰⁴(105-digit number)

63144063196652200438…54687710533310154161

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

6.314 × 10¹⁰⁴(105-digit number)

63144063196652200438…54687710533310154161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.262 × 10¹⁰⁵(106-digit number)

12628812639330440087…09375421066620308321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.525 × 10¹⁰⁵(106-digit number)

25257625278660880175…18750842133240616641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.051 × 10¹⁰⁵(106-digit number)

50515250557321760351…37501684266481233281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.010 × 10¹⁰⁶(107-digit number)

10103050111464352070…75003368532962466561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.020 × 10¹⁰⁶(107-digit number)

20206100222928704140…50006737065924933121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.041 × 10¹⁰⁶(107-digit number)

40412200445857408280…00013474131849866241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.082 × 10¹⁰⁶(107-digit number)

80824400891714816561…00026948263699732481

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Cunningham Chain of the Second 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer