Difference between revisions of "2007 iTest Problems/Problem 1"
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==Problem== | ==Problem== | ||
| − | A twin prime pair is a set of two primes <math>(p, q)</math> such that <math>q</math> is <math>2</math> greater than <math>p</math>. What is the arithmetic mean of the two primes in the smallest twin prime pair? | + | A twin prime pair is a set of two primes <math>(p, q)</math> such that <math>q</math> is <math>2</math> greater than <math>p</math>. What is the arithmetic mean of the two primes in the smallest twin prime pair? |
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==Solution== | ==Solution== | ||
Revision as of 14:57, 24 February 2020
Problem
A twin prime pair is a set of two primes 
such that 
is 
greater than 
. What is the arithmetic mean of the two primes in the smallest twin prime pair?
Solution
We consider the first few primes.
. 
isn't a prime, so this isn't a set of twin primes.
. 
is a prime, so the answer is 
.
Alternate Solution
Seeing as 
is the only choice, we determine that the answer is 
.
See Also
| 2007 iTest (Problems, Answer Key) | ||
| Preceded by: First Question |
Followed by: Problem 2 | |
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