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How do you list all the prime numbers between 80 and 90?

2 Answers
Dec 27, 2016

Answer:

You evaluate the 5 odd numbers from 81 to 89.

Explanation:

In division testing you may skip #2# now, we can also skip #5# if the number doesn't end in #5# or #0#

#81//3=27# comes out evenly

#83//3=27# and 2 left
#83//7=11# and 6 left
We don't have to test any further: 83 is prime

#85//5=19# comes out evenly

#87//3=29# comes out evenly

#89//3=29# and 2 left
#89//7=12# and 5 left
We don't have to test any further: 89 is prime

Note : We didn't have to test for the next prime 11, because if the number has a factor of 11 or higher, it also has a factor smaller than 11, and we would have found that. The highest prime you test for is smaller/equal to the square root of the number.

Aug 7, 2017

Answer:

#83 and 89#

Explanation:

To list the prime numbers between #80 and 90# we can use the rules of divisibility as a start;

#80, 81," "82," "83," "84," "85," "86," "87," "88," "89," "90#

All even numbers are divisible 2, they are not prime. apart from #2#
This leaves all the odd numbers.

#81," "83," "85," "87," "89,#

A number ending in #5# is divisible by #5#

#81," "83," "87," "89,#

If the sum of the digits is divisible by #3#, #3# is a factor

#81" "rarr 8+1=9." "# 81 is not prime

#83" "rarr 8+3 = 11" "# 83 might be prime

#87" "rarr 8+7=15" "# 87 is not prime

#89" "rarr 8+9 = 17" "#89 might be prime

As factors are always in pairs we only need to consider factors less than the square roots.

#sqrt83 = 9.....#

#2,3,4,5,6,7,8,9# are not factors: #83# is prime

#sqrt89 = 9......#

#2,3,4,5,6,7,8,9# are not factors: #89# is prime