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Q: Why can there never be a pair of consecutive prime numbers that are both prime?

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2 and 3 are consecutive numbers and they are both prime.

Consecutive prime numbers are 2 integers that differ by 1 and are both prime. Since 2 is the only even prime, 2 and 3 are the only consecutive primes.

Because one of them would necessarily be even, and therefore divisible by 2.

Both prime number

You take two consecutive odd numbers and check both of them to see whether they are prime or not.

Greater than one, numbers are either composite or prime, never both.

The only two consecutive numbers that are both prime are 2 and 3. Since there are no other even prime numbers (other than 2), there are no more pairs of consecutive prime numbers. Therefore, the term "twin primes" usually refers to pairs of prime numbers that are 2 numbers apart. Examples are (3, 5), (5, 7), (11, 13), (101, 103), and many others more. It is not currently know whether there are infinitely many twin primes.

Ah hah! You didn't say so, but you must be talking about 2 and 3 ... the only two consecutive numbers that are both prime numbers. There can't be any others. Because if you have any other two consecutive numbers, one of them has to be an even number ... divisible by 2. Since that number is divisible by 2, it's not a prime number.

Both are already Prime Numbers.5 and 13 are both prime numbers.

They both are not prime numbers

Two even numbers are never prime because all even numbers have 2 as a common factor.

Yes. 13 and 29 are both prime numbers.

yes, both 2 and 5 are prime numbers

Yes, they are both prime numbers.

Yes, both are prime numbers.

73 is the largest 2 digit number that is both prime and has prime numbers for both of its digits.

Both. Because there are both even and odd prime numbers.

23 and 29 are both prime numbers.

A prime number is a number only divisible by 1 and itself, since nothing else goes into 2 but 1 and 2 and nothing goes into 3 but 1 and 3 they are both prime and since 3 goes after 2 they are consecutiveAnd 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.1 is not a prime so that (1,2) is not a pair of consecutive integers that are prime. So, if there is another opair of consecutive numbers that are prime, they must be larger than (2,3) - ie the smaller of the pair must be greater than 2.Now any pair of consecutive numbers must have one odd and one even number. Therefore, the candidate pair must contain an even number which is greater than 2. But all even numbers greater than 2 are divisible by 2 and so are composite (non-prime). So every such candidate pair contains an odd number which may or may not be prime, and an even number which is definitely not a prime.

It is: 73 of which 7 and 3 are both prime numbers

Both are not prime numbers, but they are relatively prime.

Assuming you mean other than 2 and 3, there can't be any others because one of the two consecutive numbers would be even, in which case it is either identical to 2 or divisible by 2. Since 1 is not regarded as prime, this leaves only 2 and 3.

No. They are both composite numbers. They are not relatively prime either.

5 and 7 are both prime numbers.

They are 71 and 73 which are both prime numbers