How many integers E are prime numbers in the range 200 < E < 220?
Select
A) 1  B) 2  C) 3  D) 4  E) 5
My friend, every single odd number greater than can be written either as 4E+1 or as 4E+3. If you divide any odd number by 4, you will get a remainder of either 1 or 3. That's not a rule unique to prime numbers at all.   The 6E+1 or 6E-1 rule is basically every odd number that is not divisible by three, so it narrows the search a little.   Here's how I thought about the problem. First, eliminate all the even numbers and the odd multiples of 5 in that range. That leaves us with:   {201, 203, 207, 209, 211, 213, 217, 219}   Eliminate the four multiples of 3. Notice that 21 is a multiple of 3, so 210 is also a multiple of 3. If we add or subtract 3 or 9, we get more multiples of three. When we eliminate those, we are left with.   {203, 209, 211, 217}   Now, notice that a cool thing about this range is that 210 is also a multiple 7 (again, because 21 is a multiple of 7). This means that    210 - 7= 
<gadget id="calculator"> 210 - 7</gadget>
<output>203</output>
203   210 + 7= 
<gadget id="calculator">210 + 7</gadget>
<output>217</output>
217   Those two numbers are also multiples of 7, so eliminate them from the list. Now, we are left with   {209, 211}.   We've already checked all the prime numbers less than 10, so we know that neither of these numbers is divisible by anything less than 10. We have to check 11 now. We know that 22 is a multiple of 11, so 220 is also a multiple of 11. This means that    220 - 11= 
<gadget id="calculator"> 220 - 11</gadget>
<output>209</output>
209   is also a multiple of 11. We can eliminate this from the list also.   That leaves us with just 211. There's no zero option in the question, so this must be a prime number.   1nswer= (1)
<result>A</result>
How many integers E are prime numbers in the range 200 < E < 220?