Block #358,943

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/14/2014, 11:18:06 AM · Difficulty 10.3840 · 6,440,423 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c6b0302305db064b4fe94c6176a92a9251206772b89bec825ec43080103bee48

View on Chainz ↗

Height

#358,943

Difficulty

10.384027

Transactions

Size

1.14 KB

Version

Bits

0a624f93

Nonce

465,177

Timestamp

1/14/2014, 11:18:06 AM

Confirmations

6,440,423

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

e4a644959f5471f7e5d5db6822e02dbf988c7de5b3c5b6f9a3c9a05e885f86ba

Transactions (2)

Coinbase82189476a66fd9…d92c4901c8ba54

1 in → 1 out9.2700 XPM110 B

AeKNrjNj…1NEq95Ta

d31c965955c59f…704acc59f4eb81

6 in → 2 out12.0931 XPM964 B

AHoPoZnL…KYXkkW8Y AMtVLNcn…XDi8pAcb

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.

5.758 × 10⁹⁵(96-digit number)

57580139815229049677…59396728657735723521

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

5.758 × 10⁹⁵(96-digit number)

57580139815229049677…59396728657735723521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.151 × 10⁹⁶(97-digit number)

11516027963045809935…18793457315471447041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.303 × 10⁹⁶(97-digit number)

23032055926091619871…37586914630942894081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.606 × 10⁹⁶(97-digit number)

46064111852183239742…75173829261885788161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.212 × 10⁹⁶(97-digit number)

92128223704366479484…50347658523771576321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.842 × 10⁹⁷(98-digit number)

18425644740873295896…00695317047543152641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.685 × 10⁹⁷(98-digit number)

36851289481746591793…01390634095086305281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.370 × 10⁹⁷(98-digit number)

73702578963493183587…02781268190172610561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.474 × 10⁹⁸(99-digit number)

14740515792698636717…05562536380345221121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.948 × 10⁹⁸(99-digit number)

29481031585397273434…11125072760690442241

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