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All even numbers greater than 2 are composite because they are all divisible by 2. Therefore, from 3 onwards, all prime numbers are odd.
Consider three consecutive odd numbers. They must be of the form 2n+1, 2n+3 and 2n+5 where n is an integer.
Since n is an integer, n will leave a remainder of 0, 1 or 2 when it is divided by 3.
Suppose n leaves a remainder of 0 when divided by 3. Therefore n = 3k for some integer k. Then 2n+3 = 2*(3k) + 3 = 6k + 3 = 3*(2k+1). That is, middle of the three consecutive odd numbers is divisible by 3 and so it is not a prime.
Now, suppose n leaves a remainder of 1 when divided by 3. Therefore n = 3k+1 for some integer k. Then 2n+1 = 2*(3k+1) + 1 = 6k+2+1 = 6k+3 = 3*(2k+1). That is, first of the three consecutive odd numbers is divisible by 3 and so it is not a prime.
Finally, suppose n leaves a remainder of 2 when divided by 3. Therefore n = 3k+2 for some integer k. Then 2n+5 = 2*(3k+2) + 5 = 6k+4+5 = 6k+9 = 3*(2k+3). That is, last of the three consecutive odd numbers is divisible by 3 and so it is not a prime.
Thus for any three consecutive odd numbers greater than 3, one of them is divisible by 3 and therefore the three cannot all be prime.
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What is the Product of two consecutive prime numbers?
There is only one pair of consecutive prime numbers, and the prime numbers are two and three, because any pair of consecutive numbers has one odd and one even number, and two is the only even prime number, because all other even numbers can be divided by two, and the only pairs of consecutive numbers are one and two and three, but one is not prime because it only has one factor, thus making the only consecutive pair of primes two and three. But the problem asks for the product of the two numbers, not the numbers themselves, so just multiply two and three together to get a final result of six.
What does consecutive prime numbers mean?
2 and 3 are the only consecutive prime numbers.
What are two consecutive prime numbers called?
2 and 3 are the only consecutive numbers that are prime.
What is the only prime number that is the sum of four consecutive prime numbers?
17 is the only prime number that is the sum of four consecutive prime numbers. 2 + 3 + 5 + 7 = 17
Why are 2 and 3 the only consecutive prime numbers?
And they are the ONLY consecutive prime numbers because if you have one prime number (i.e. 29), then there always is an even number right after the prime number (i.e. 30 comes right after 29), and consecutive means "right next to," right? And we all know that even numbers can always be divided in half, so 2 and 3 are the only consecutive prime numbers.
Can you get three consecutive prime numbers?
Only 1 2 3
How do you get consecutive prime numbers?
The only consecutive prime numbers are 2 and 3.
What is the Product of two consecutive prime numbers?
There is only one pair of consecutive prime numbers, and the prime numbers are two and three, because any pair of consecutive numbers has one odd and one even number, and two is the only even prime number, because all other even numbers can be divided by two, and the only pairs of consecutive numbers are one and two and three, but one is not prime because it only has one factor, thus making the only consecutive pair of primes two and three. But the problem asks for the product of the two numbers, not the numbers themselves, so just multiply two and three together to get a final result of six.
What are prime consecutive numbers?
2 and 3 are the only example of consecutive prime numbers.
What does consecutive prime numbers mean?
2 and 3 are the only consecutive prime numbers.
Why 35 and 7 are the only three consecutive odd prime numbers?
If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.If you take three consecutive odd (or three consecutive even) numbers, one of the three will always be a multiple of 3.
What are two consecutive prime numbers called?
2 and 3 are the only consecutive numbers that are prime.
What are All the consecutive prime numbers to 100?
2 and 3 are the only consecutive numbers that are prime.
Why are two and three the only consecutive prime numbers?
The number 2 is the only even prime number - all other even numbers are divisible by 2.
What are pair of consecutive prime numbers?
2 and 3 are consecutive numbers that are prime.
What are consecutive prime?
2 and 3 are the only consecutive prime numbers.
Can 3 consecutive whole numbers be primes?
No. Any three consecutive numbers will have at least one of them which is divisible by 2, which means it cannot be prime. And since 1 is not considered a prime number, it cannot happen.
