Difference between revisions of "2007 iTest Problems/Problem 1"
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<math>(2,2+2)\equiv (2,4)</math>. <math>4</math> isn't a prime, so this isn't a set of twin primes. | <math>(2,2+2)\equiv (2,4)</math>. <math>4</math> isn't a prime, so this isn't a set of twin primes. | ||
| − | <math>(3,3+2)\equiv (3,5)</math>. <math>5</math> is a prime, so the answer is <math>\frac{3+5}{2}=4 | + | <math>(3,3+2)\equiv (3,5)</math>. <math>5</math> is a prime, so the answer is <math>\frac{3+5}{2}=4</math>. |
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| + | ==Cheap Solution== | ||
| + | Note that <math>A</math> is the only answer choice offered, so you must choose it. | ||
| + | |||
==See Also== | ==See Also== | ||
{{iTest box|year=2007|before=First Question|num-a=2}} | {{iTest box|year=2007|before=First Question|num-a=2}} | ||
[[Category:Introductory Number Theory Problems]] | [[Category:Introductory Number Theory Problems]] | ||
Latest revision as of 11:33, 29 January 2021
Contents
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 
.
Cheap Solution
Note that 
is the only answer choice offered, so you must choose it.
See Also
| 2007 iTest (Problems, Answer Key) | ||
| Preceded by: First Question |
Followed by: Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • TB1 • TB2 • TB3 • TB4 | ||
