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Block #300,795

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/8/2013, 7:18:01 PM · Difficulty 9.9924 · 6,513,077 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4ed231be47cf281d2a5a9b355264c5f26e00c4d834e811381a95fb76c33a3e17

View on Chainz ↗

Height

#300,795

Difficulty

9.992393

Transactions

Size

1.82 KB

Version

Bits

09fe0d77

Nonce

26,261

Timestamp

12/8/2013, 7:18:01 PM

Confirmations

6,513,077

Merkle Root

c647f3ffe38fe69a0e1eb85d192b08f0cfd0728b383ed35c6ceca37411e076bd

Transactions (4)

Coinbase4faeb619441766…bdf99d90b5b891

1 in → 27 out9.9772 XPM981 B

AGPYJBwg…5yWMRKmU AQf7sjuh…sNY5fXpu AYtDvcGs…VuAcA7m7 AYcLTeXR…bscgPops AZ2pPuKg…95SN2Yr7

b1b4ec6e7f1821…c2c35a4ebbe0ba

1 in → 2 out1453.3622 XPM226 B

AXBHrg2z…zanE6mez AabJgmhW…MxUCvA12

d87b25054ab269…f316564dbd086e

2 in → 1 out0.2600 XPM338 B

AXfe1a7Z…BgWghXd7

02881d09834926…ccb7258a7e3f39

1 in → 2 out1452.3473 XPM227 B

ANsQMtN9…8ZeDMwWp AXr6dQsr…ZQAd526C

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.

3.106 × 10⁹¹(92-digit number)

31069733162143104872…68764656720180013320

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

3.106 × 10⁹¹(92-digit number)

31069733162143104872…68764656720180013321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.213 × 10⁹¹(92-digit number)

62139466324286209744…37529313440360026641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.242 × 10⁹²(93-digit number)

12427893264857241948…75058626880720053281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.485 × 10⁹²(93-digit number)

24855786529714483897…50117253761440106561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.971 × 10⁹²(93-digit number)

49711573059428967795…00234507522880213121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.942 × 10⁹²(93-digit number)

99423146118857935591…00469015045760426241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.988 × 10⁹³(94-digit number)

19884629223771587118…00938030091520852481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.976 × 10⁹³(94-digit number)

39769258447543174236…01876060183041704961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.953 × 10⁹³(94-digit number)

79538516895086348473…03752120366083409921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.590 × 10⁹⁴(95-digit number)

15907703379017269694…07504240732166819841

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.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

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, …

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 300795

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 4ed231be47cf281d2a5a9b355264c5f26e00c4d834e811381a95fb76c33a3e17

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #300,795 on Chainz ↗

Block #300,795

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