Block #359,826

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/15/2014, 1:32:51 AM · Difficulty 10.3877 · 6,466,749 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

d1aeafa4e3c2baf4eac11080d30c8fbaa138b8d98b07894831fb4974271f0ef5

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Height

#359,826

Difficulty

10.387698

Transactions

Size

205 B

Version

Bits

0a63402c

Nonce

148,889

Timestamp

1/15/2014, 1:32:51 AM

Confirmations

6,466,749

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

5d48ad161d291dad4562a61438e15ca21894c5cddccac74db2fa341038c564d3

Transactions (1)

Coinbase5d48ad161d291d…fa341038c564d3

1 in → 1 out9.2500 XPM110 B

AeKNrjNj…1NEq95Ta

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.

1.568 × 10¹⁰⁶(107-digit number)

15682611217422557558…19202780678323005441

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

1.568 × 10¹⁰⁶(107-digit number)

15682611217422557558…19202780678323005441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.136 × 10¹⁰⁶(107-digit number)

31365222434845115117…38405561356646010881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.273 × 10¹⁰⁶(107-digit number)

62730444869690230234…76811122713292021761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.254 × 10¹⁰⁷(108-digit number)

12546088973938046046…53622245426584043521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.509 × 10¹⁰⁷(108-digit number)

25092177947876092093…07244490853168087041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.018 × 10¹⁰⁷(108-digit number)

50184355895752184187…14488981706336174081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.003 × 10¹⁰⁸(109-digit number)

10036871179150436837…28977963412672348161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.007 × 10¹⁰⁸(109-digit number)

20073742358300873674…57955926825344696321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.014 × 10¹⁰⁸(109-digit number)

40147484716601747349…15911853650689392641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

8.029 × 10¹⁰⁸(109-digit number)

80294969433203494699…31823707301378785281

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

Block #359,826

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