Perfect numbers cannot be prime numbers. Here's why:
A number N is perfect if σ(N) = 2N (σ is the sum of divisors function). If there is a prime p that is a perfect number, then σ(p) = 2p. However, the only factors of p are 1 and p, so σ(p) is also equal to p+1. If 2p = p+1, then p=1, which is not prime, and 1 is defined to have only one factor, 1.
Prime numbers have two factors. The sum of their proper divisors is always 1.
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, all prime numbers are deficient.
A [perfect] square number, by definition, has a factor which is its square root. As a result it CANNOT be a prime!
So far 47. Euler proved that every even perfect number will be of the form 2p−1(2p−1), where p is prime and 2p−1 is also prime. If 2p−1 is prime it is known as a Mersenne prime. Since 47 Mersenne primes are known, 47 even perfect numbers are known. As for odd perfect numbers, none are known, nor has it been proven yet that there aren't any.
They really are not
Prime numbers have two factors. The sum of their proper divisors is always 1.
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, all prime numbers are deficient.
Any number squared except 0 is a perfect square so it follows that prime numbers are less common than perfect squares.
No because technically its different .
Just 1.
A [perfect] square number, by definition, has a factor which is its square root. As a result it CANNOT be a prime!
So far 47. Euler proved that every even perfect number will be of the form 2p−1(2p−1), where p is prime and 2p−1 is also prime. If 2p−1 is prime it is known as a Mersenne prime. Since 47 Mersenne primes are known, 47 even perfect numbers are known. As for odd perfect numbers, none are known, nor has it been proven yet that there aren't any.
44,100
No - prime numbers are numbers that can only be divided by 1 and itself. 25 and 49 are examples of perfect squares 5*5 = 25 and 7*7=49
The prime numbers: 2, 3, 5, 7, 11, 13, 17, 19