No, all prime numbers are deficient.
A perfect number cannot be a prime.
1 is not considered a prime number; 1 is a perfect square.
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.
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.
because it needs to be a prime number and it has to be simplified
A perfect number cannot be a prime.
A perfect number is a positive integer whose factors (excluding the number itself) add up the number; 6 is a perfect number: 1 x 2 x 3 = 6 1 + 2 + 3 = 6 Prime numbers, by definition, don't have factors, so cannot be perfect. In fact, it may be that odd numbers can't be perfect.
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.
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.
No. A prime number is always odd.
No.
It is not possible for any multiple of a prime number to be prime.
1 is not considered a prime number; 1 is a perfect square.
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.
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.
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Nice question! The square root of (any number that isn't a perfect square) is irrational. No prime number is a perfect square. So the square root of any prime number is irrational.