Can the mean of 2 consecutive prime numbers be prime?

Can the mean of any two consecutive prime numbers ever be prime? By definition of mean the result must be between the two source numbers. By definition of consecutive there can’t be a prime number in between two consecutive prime numbers.

What is the mean of two consecutive prime numbers?

Aside from 2, all other prime numbers are odd. So the mean of any consecutive prime number is of course even and hence divisible by 2.

Is the sum of any two consecutive prime numbers also prime?

No. The only 2 consecutive prime numbers whose sum is a prime are 2 and 3. The sum of any other 2 consecutive primes (which are all ODD numbers) will be an EVEN number, and thus not prime.

Can two consecutive whole numbers be prime numbers?

2 and 3 are only consecutive prime numbers as 2 is the only even prime number and after that each consecutive pair contains one even and another odd number.

What are two consecutive prime numbers that differ from 2?

Answer: Three pairs of prime numbers whose difference is 2 are (5, 7), (11, 13) and (17, 19). A pair of prime numbers whose difference is 2 are called twin primes.

What do you mean by consecutive prime numbers?

Define a series of consecutive prime numbers to be a series of numbers, each prime, in which there are no other prime numbers between them. These are not necessarily consecutive numbers themselves. For example, the numbers 5,7 and 11 are consecutive prime numbers, although they are not consecutive numbers.

What does consecutive number mean?

Consecutive numbers are numbers that follow each other in order from the smallest number to the largest number. The difference between consecutive numbers is always fixed and it follows a pattern. For example 1, 2, 3 are the first three consecutive natural numbers.

Are two consecutive numbers always relatively prime?

Consecutive positive integers are always relatively prime, since, if a prime divides both and , then it must divide their difference , which is impossible since . Two integers and are relatively prime if and only if there exist some such that (a special case of Bezout’s Lemma).

Does the sum of two prime numbers equal a prime number?

Any two consecutive integers are always coprime. Sum of any two coprime numbers is always coprime to their product. 1 is trivially coprime with all numbers. if out of two numbers, any one number is a prime number while other number is not a multiple of first one, then both are coprime.

Is two the only even prime number?

Quick Answer. Two is the only even prime number because other even numbers have at least three or more positive divisors. A number can only be considered prime when it only has two positive divisors: itself and 1.

What are the two lowest prime numbers?

A prime number must have exactly two factors (1 and itself). Therefore, the number 2 is the lowest prime number as its only common divisors are 1 and 2. The number 1 only has 1 common divisor so it cannot be a prime number.