Block #497,594

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/17/2014, 4:25:27 PM · Difficulty 10.7692 · 6,301,561 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

12ee6bc6e167c9aab5d43e4145641b769f6149ed53fabbe2ac8c4db1413b6a2e

View on Chainz ↗

Height

#497,594

Difficulty

10.769195

Transactions

Size

869 B

Version

Bits

0ac4e9f3

Nonce

2,097

Timestamp

4/17/2014, 4:25:27 PM

Confirmations

6,301,561

Mined by

⛏️ aSPrAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

159a5fcf66287cd665e6234c85c3a533a7a40f129a127592a9084e7a8252f684

Transactions (1)

Coinbase159a5fcf66287c…084e7a8252f684

1 in → 21 out8.6100 XPM777 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j AQyr8Lw3…hs4nt3Pn

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.

4.519 × 10⁹⁹(100-digit number)

45193719967057751264…74964568998572891361

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

4.519 × 10⁹⁹(100-digit number)

45193719967057751264…74964568998572891361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

9.038 × 10⁹⁹(100-digit number)

90387439934115502528…49929137997145782721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.807 × 10¹⁰⁰(101-digit number)

18077487986823100505…99858275994291565441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.615 × 10¹⁰⁰(101-digit number)

36154975973646201011…99716551988583130881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.230 × 10¹⁰⁰(101-digit number)

72309951947292402023…99433103977166261761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.446 × 10¹⁰¹(102-digit number)

14461990389458480404…98866207954332523521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.892 × 10¹⁰¹(102-digit number)

28923980778916960809…97732415908665047041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.784 × 10¹⁰¹(102-digit number)

57847961557833921618…95464831817330094081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.156 × 10¹⁰²(103-digit number)

11569592311566784323…90929663634660188161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.313 × 10¹⁰²(103-digit number)

23139184623133568647…81859327269320376321

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer