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Is the sum of any two prime numbers always a composite number?
The sum of any two prime numbers is not always a composite number. The sum of 2 and 11 is 13, and 13 is a prime number, not a composite number.
Are any two prime numbers relatively prime?
Any two prime numbers will be relatively prime. Numbers are relatively prime if they do not have any prime factors in common. Prime numbers have only themselves as prime factors, so all prime numbers are relatively prime to the others.
Why arent there any other consecutive prime numbers besides 2 and 3?
Because any consecutive pair of numbers would involve an even number which will always be divisible by 2. As 2 is the only even prime number, 2 and 3 are necessarily the only sequential prime numbers.
Why are the multiples of any number other than one not prime numbers?
The multiples of any number cannot be prime numbers because such numbers are the product of at least two numbers. Prime numbers, but definition, cannot be cannot be the product of any numbers except itself and one.
Why is the gcf of two prime numbers always 1?
Because they don't have any other factors in common.
Can any two prime numbers be relatively prime?
It is, and always is relatively prime.
Is the sum of any two prime numbers always a composite number?
The sum of any two prime numbers is not always a composite number. The sum of 2 and 11 is 13, and 13 is a prime number, not a composite number.
Are there any pairs of prime numbers that when multiplied do not make their least common multiple?
The product of all pairs of prime numbers is always the least common multiple of the two prime numbers.
Are any two prime numbers relatively prime?
Any two prime numbers will be relatively prime. Numbers are relatively prime if they do not have any prime factors in common. Prime numbers have only themselves as prime factors, so all prime numbers are relatively prime to the others.
Is 550 a composite or prime number?
Any even number is always divisible by 2 and thus (apart from 2 itself) all even numbers can not be prime numbers.
Is it true that the product of any two prime numbers are always odd?
Not always because as for example 2*19 = 38
What two number pairs whose least common factor is the product of the number?
Any pair of prime or relatively prime numbers.
Can a GCF of two primes numbers be 1?
Yes because 1 is a factor of any prime number. In fact, 1 is always the gcd (same as gcf) of any two distinct prime numbers.
Will a prime number always be coprime with any other whole number?
No. Consider 2 and all other even numbers. Consider multiples of prime numbers, like 3 and 9.
Why arent there any other consecutive prime numbers besides 2 and 3?
Because any consecutive pair of numbers would involve an even number which will always be divisible by 2. As 2 is the only even prime number, 2 and 3 are necessarily the only sequential prime numbers.
How can you prove there is no largest prime number?
No. No matter how large of an example you choose, someone always can find a larger number (of any kind), because the upper range of number is infinite. If you take all the known prime numbers and multiply them together, then add 1 to the result, you will have a number that is not divisible by any of the known prime numbers. This number will either be prime or have prime factors that were not previously known. So, in this way, you can always find a new prime number or a number that is a multiple of new prime numbers. If the known prime numbers include all the prime numbers up to the largest known, the new ones must be larger.
Why are square numbers one less than a prime number always even?
Prime numbers, except 2, are always odd (they would not be prime if they were even cos they would be divisible by 2.) 1 less than any odd number must be an even number.
