Home/Chain Registry/Block #2,682,300

Block #2,682,300

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/29/2018, 12:40:25 AM · Difficulty 11.6913 · 4,157,504 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f4120efcdf3575a715c75d4050c992a7e708e7de8939121c3083c2f816d36988

View on Chainz ↗

Height

#2,682,300

Difficulty

11.691315

Transactions

Size

923 B

Version

Bits

0bb0fa0d

Nonce

197,833,264

Timestamp

5/29/2018, 12:40:25 AM

Confirmations

4,157,504

Merkle Root

96a2a96a27fefc40db02ea50d6a6504f8937edb3b4340196793476a3685eb707

Transactions (4)

Coinbasec7f3374ec993b3…3ec9eb76df5cfe

1 in → 1 out7.3300 XPM110 B

AZzj3KBC…TncGTg2f

16c5861946af9b…37d5f40415e68a

1 in → 2 out7.2900 XPM192 B

AJMrMUVA…XLVBXChy AG2qwuzZ…RZWfWy1T

f785e5b2968a26…b2e40d1ae3d3da

1 in → 2 out7.2900 XPM192 B

AHtKGoRa…s5Shmq9n ANWVVTZm…NH9wfNti

efb43408ccf43e…8d70cb34fe7ffd

2 in → 2 out13.5678 XPM339 B

AJLjNEZe…ufZNC9G5 AGzrd4MM…7HC9qVLn

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.

5.111 × 10⁹⁴(95-digit number)

51116312100346338465…24132039748085770240

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

5.111 × 10⁹⁴(95-digit number)

51116312100346338465…24132039748085770239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.022 × 10⁹⁵(96-digit number)

10223262420069267693…48264079496171540479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.044 × 10⁹⁵(96-digit number)

20446524840138535386…96528158992343080959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.089 × 10⁹⁵(96-digit number)

40893049680277070772…93056317984686161919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.178 × 10⁹⁵(96-digit number)

81786099360554141545…86112635969372323839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.635 × 10⁹⁶(97-digit number)

16357219872110828309…72225271938744647679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.271 × 10⁹⁶(97-digit number)

32714439744221656618…44450543877489295359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.542 × 10⁹⁶(97-digit number)

65428879488443313236…88901087754978590719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.308 × 10⁹⁷(98-digit number)

13085775897688662647…77802175509957181439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.617 × 10⁹⁷(98-digit number)

26171551795377325294…55604351019914362879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

5.234 × 10⁹⁷(98-digit number)

52343103590754650589…11208702039828725759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First 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

RareChain length 11

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 1CC formula:

1CC: 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 2682300

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 f4120efcdf3575a715c75d4050c992a7e708e7de8939121c3083c2f816d36988

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 #2,682,300 on Chainz ↗

Block #2,682,300

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