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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.

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Q: Why are no prime number a perfect number?

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A perfect number cannot be a prime.

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.

No. A prime number is always odd.

No, all prime numbers are deficient.

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.

1 is not considered a prime number; 1 is a perfect square.

16

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.

No, being a perfect cube would mean it has factors.

because it needs to be a prime number and it has to be simplified

3 is prime, 1 less than the perfect square of 4 (2x2)

4, 16, 64 and many others

16.

16

The number is 16.

16

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.

Perfect numbers have the form 2n-1(2n-1) where 2n-1 is a Mersenne prime. When a new Mersenne prime is discovered, so is a new perfect number.

No, it's a perfect square 73 * 73.

That is correct.

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.

Any such number has a perfect square factor.If you want examples, just multiply some prime factors together, making sure that at least one is repeated.

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.

There is only one Perfect Number within this range : 496. If 2ⁿ - 1 is prime then 2ⁿ⁻¹(2ⁿ - 1) is a perfect number. In this instance n = 5 then, 2⁴(2⁵ - 1) = 16 x 31 = 496...........and 31 is a prime number.