Block #345,916

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/6/2014, 6:07:43 AM · Difficulty 10.2141 · 6,450,968 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

3edbccebdc859cdc838572bea0ad19b32c3e615c2584404f79089408c5d10d84

View on Chainz ↗

Height

#345,916

Difficulty

10.214099

Transactions

Size

1.05 KB

Version

Bits

0a36cf33

Nonce

3,301

Timestamp

1/6/2014, 6:07:43 AM

Confirmations

6,450,968

Mined by

⛏️ <GaRHAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

9e93d52c76a31595fc988bbb8c75b5aa85937e338c50cd6b252df051dcf769fd

Transactions (1)

Coinbase9e93d52c76a315…2df051dcf769fd

1 in → 27 out9.5700 XPM981 B

AQvZBsUo…hppgRZTJ AQwRN8bE…V8PsTcY9 Ad9pSzHt…cpJ3y2zz APeshfYV…3PKcKMKH AZemWJAo…6jhDtieG

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.

1.210 × 10⁹⁹(100-digit number)

12105284647167891461…65114680104840283521

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

1.210 × 10⁹⁹(100-digit number)

12105284647167891461…65114680104840283521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.421 × 10⁹⁹(100-digit number)

24210569294335782922…30229360209680567041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.842 × 10⁹⁹(100-digit number)

48421138588671565845…60458720419361134081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.684 × 10⁹⁹(100-digit number)

96842277177343131690…20917440838722268161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.936 × 10¹⁰⁰(101-digit number)

19368455435468626338…41834881677444536321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.873 × 10¹⁰⁰(101-digit number)

38736910870937252676…83669763354889072641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.747 × 10¹⁰⁰(101-digit number)

77473821741874505352…67339526709778145281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.549 × 10¹⁰¹(102-digit number)

15494764348374901070…34679053419556290561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.098 × 10¹⁰¹(102-digit number)

30989528696749802141…69358106839112581121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.197 × 10¹⁰¹(102-digit number)

61979057393499604282…38716213678225162241

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