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A perfect number cannot be a prime.
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Is there a product of two perfect squares that is not a perfect square?
No there isn't. every perfect square number can be factored into prime number. At their factoration you'll always have multiples of two on the primes exponent. Therefore you'll multiply a prime raised to a 2-multiple number with another prime raised to a 2-multiple number wich gives you also a number that factored gives you a product of prime numbers raised to a 2-multiple number and so, a perfect square.
Is it possible for a prime number to be a perfect number and why?
No, all prime numbers are deficient.
What is special about a Mersenne prime?
A Mersenne prime has the form 2n-1. For 2n-1 to be prime, n must also be prime. Perfect numbers have the form 2n-1(2n-1) where 2n-1 is a Mersenne prime, so when a new Mersenne prime is discovered, another perfect number is also found.
Is 1 a prime number or a square number?
1 is not considered a prime number; 1 is a perfect square.
Why are no prime number a perfect number?
The only factors of a prime are 1 and itself. So, the only factor smaller than the number itself is 1. Therefore the sum of all factors smaller than the number is 1. But 1 is not a prime number. Thus, there is no prime number that is a perfect number.
Is one a perfect number?
no, but I don't know why. One is not a prime number and by definition of a perfect number one must be a prime number.
Is 13 a perfect number?
No, it is not.Incidentally, is a number p is prime then its 2 factors are 1 and p. Their sum is p+1.If p is a perfect number then this sum must be 2p.That is, p+1 = 2p or p = 1.But 1 is not a prime. So no prime can be a perfect number and since 13 is prime, it cannot be a perfect number.
Is there a product of two perfect squares that is not a perfect square?
No there isn't. every perfect square number can be factored into prime number. At their factoration you'll always have multiples of two on the primes exponent. Therefore you'll multiply a prime raised to a 2-multiple number with another prime raised to a 2-multiple number wich gives you also a number that factored gives you a product of prime numbers raised to a 2-multiple number and so, a perfect square.
Can a perfect square be a prime number Explain?
No. A prime number is always odd.
Is it possible for a prime number to be a perfect number and why?
No, all prime numbers are deficient.
No prime number can be a perfect square True or false?
True. By definition, a prime number is divisible by one and by itself. Also by definition, a perfect square has at least an additional pair of factors - it's square root. Therefore a prime number could never be a perfect square. One exception that might come to mind in this case is the number one. One however, is not considered a prime number, and thus does not conflict with this rule.
Can a prime number be a perfect square?
No.
Can a prime number be a perfect cube?
Sure, honey, let me break it down for you. No, a prime number cannot be a perfect cube because a prime number is only divisible by 1 and itself. And let me tell you, a perfect cube is the result of multiplying a number by itself three times, so a prime number ain't gonna fit that bill. So, in short, a prime number and a perfect cube are like oil and water - they just don't mix, darling.
What is special about a Mersenne prime?
A Mersenne prime has the form 2n-1. For 2n-1 to be prime, n must also be prime. Perfect numbers have the form 2n-1(2n-1) where 2n-1 is a Mersenne prime, so when a new Mersenne prime is discovered, another perfect number is also found.
Is 1 a prime number or a square number?
1 is not considered a prime number; 1 is a perfect square.
Why are no prime number a perfect number?
The only factors of a prime are 1 and itself. So, the only factor smaller than the number itself is 1. Therefore the sum of all factors smaller than the number is 1. But 1 is not a prime number. Thus, there is no prime number that is a perfect number.
What square numbers below 100 are also prime numbers?
A [perfect] square number, by definition, has a factor which is its square root. As a result it CANNOT be a prime!
