Solve the Problem $\mathrm { n } ^ { 2 } - \mathrm { n } + 41$

question 22

Short Answer

Solve the problem.
-Euler conjectured that the formula $\mathrm { n } ^ { 2 } - \mathrm { n } + 41$ would generate prime numbers for whole numbers $\mathrm { n }$ . The formula generates prime numbers for $\mathrm { n }$ up to 40 and fails at $\mathrm { n } = 41$ .
Evaluate Euler's formula for $n = 42$ and determine whether this is a prime number. If it is not a prime number, give its prime factors.

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Definitions:

Negative Exponential Distribution

A probability distribution used to model time between events in a Poisson process, often applied in reliability engineering and queuing theory.

Arrival Rates

The frequency at which entities arrive at a particular system or service point, commonly used in queueing theory and service process analysis.

Service Times

The duration required to complete a specific service task or process, critical in evaluating service efficiency and customer satisfaction.

Waiting-Line System

A mathematical model used to analyze lines or queues in order to minimize waiting times and improve service efficiency.