Edwin R.

asked • 09/14/18

The sum of any two consecutive prime numbers is also prime.

The conjectures of the Geometry math 

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Arturo O. answered • 09/14/18

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Student,
 
Do you mean 2 consecutive numbers that are prime, or just any 2 primes that are consecutive?  It makes a difference in the answer.  For example, 7 and 11 are prime numbers that are consecutive among the prime numbers (but not consecutive among the integers), since there are no other prime numbers in between them (8, 9, and 10 are not prime numbers).  But 
 
7 + 11 = 18,
 
which is not a prime number.  As worded, there is room to interpret the question as the numbers not necessarily being consecutive among the integers, but consecutive among the prime numbers. 
 
 
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Arturo O.

Another thing to keep in mind:
 
With the exception of 2, all prime numbers are odd, the sum of two odd numbers is even, and all even numbers are divisible by 2, and hence not prime (with the exception of 2).
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09/14/18

Michael V. answered • 09/14/18

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The equation of 2+3=5 will meet your stated rules of "the sum of any two consecutive prime numbers is also prime."
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Mark M.

Yet not the word "any."
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09/14/18

Arturo O.

It is an example that meets the conditions, but it is not a proof.  Unfortunately, it is not clear from the wording of the question whether the student just wanted an example, or was asking a TRUE/FALSE question.
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09/14/18

Jordi A.

Since 2 & 3 are the one and only possible case of a pair of prime numbers which are also consecutive numbers, it turns out that "any consecutive prime numbers" is equivalent to "2 and 3", because there is no other case of consecutive prime numbers. In other words, any other pair of prime numbers different than 2 and 3 will never be consecutive because all prime numbers, with the exception of 2, are odd, and two odd numbers can never be consecutive, as numbers alternate between even and odd as you count them. For this reason, 2+3=5 is not only an example that meets the condition, but also an example that meets the condition in any possible case (which happens to be only one case, 2 and 3), and therefore serves as a proof for the statement.
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03/25/22

Jordi A.

For the reasons above, if you interpret consecutive as consecutive among the whole set of integer numbers, and not consecutive among the set of prime numbers, the statement is TRUE.
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03/25/22

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