I like prime numbers

Number Theory Level 1

Let that (Q),(R) \text{Let that (Q),(R)} are prime numbers.

Is it possible that (Q)×(R) = (prime number) \text{(Q)×(R) = (prime number)} ?

No Yes Depend Not enough information

Matin Naseri by Matin Naseri , 17, Afghanistan

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2 solutions

Matin Naseri
Feb 20, 2018

prime numbers

Suppose that : (Q)×(R) = (M = prime) \text{(Q)×(R) = (M = prime)}

The set of divisors of (M) = [1,Q,R,M] \text{The set of divisors of (M) = [1,Q,R,M]} But prime numbers must be have at most (2) \text{(2)} divisors [Prime numer,1] , but mentioned set has (4) \text{(4)} elements .

∴ \therefore M = must be a non-prime number \text{M = must be a non-prime number} .

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nice & short.

Mohammad Khaza - 3 years, 3 months ago
Durgaprasad Sahu
Feb 20, 2018

The product of two prime numbers can't be a prime number because if it is so then this violates the definition of a prime number as this product will have two factors other than 1 and the number itself.

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