Block #149,612

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/4/2013, 12:03:49 PM · Difficulty 9.8572 · 6,645,154 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

db51ccc56f30344e923cd750f6fe100fc63f38140e98391092230efb05081b1e

View on Chainz ↗

Height

#149,612

Difficulty

9.857203

Transactions

Size

2.35 KB

Version

Bits

09db71ae

Nonce

210,564

Timestamp

9/4/2013, 12:03:49 PM

Confirmations

6,645,154

Mined by

⛏️ P2SHAJQ1aTBySnuwnLtsc8mHdZcsu2oyXa68D5

Merkle Root

d1342ce98afa5a0dfa20979f59db4553f864aea8851ae7fbef210c608cc59ca5

Transactions (2)

Coinbase6f8951df7028fb…d256682f3f1440

1 in → 1 out10.3100 XPM109 B

AJQ1aTBy…oyXa68D5

45006a069645b4…cb1aec6705a281

19 in → 1 out195.8500 XPM2.16 KB

AJs27LEf…M76myr9t

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.

1.593 × 10⁹¹(92-digit number)

15939243956354869723…32885647274320209921

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

1.593 × 10⁹¹(92-digit number)

15939243956354869723…32885647274320209921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.187 × 10⁹¹(92-digit number)

31878487912709739447…65771294548640419841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.375 × 10⁹¹(92-digit number)

63756975825419478894…31542589097280839681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.275 × 10⁹²(93-digit number)

12751395165083895778…63085178194561679361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.550 × 10⁹²(93-digit number)

25502790330167791557…26170356389123358721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.100 × 10⁹²(93-digit number)

51005580660335583115…52340712778246717441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.020 × 10⁹³(94-digit number)

10201116132067116623…04681425556493434881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.040 × 10⁹³(94-digit number)

20402232264134233246…09362851112986869761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.080 × 10⁹³(94-digit number)

40804464528268466492…18725702225973739521

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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