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The sum of all prime numbers between 60 and 90 is:
610
523
373
460
523
List all odd numbers between 60 and 90, eliminate multiples of 3 and 5, and sum the remaining primes: 61, 67, 71, 73, 79, 83, 89.
Range of numbers: between 60 and 90
S=∑p∈Primesp
List all odd numbers between 60 and 90, eliminate multiples of 3 and 5, and sum the remaining primes: 61, 67, 71, 73, 79, 83, 89.
Including 60 or 90, or including non-prime numbers ending in 3 or 9 (such as 69, 81, or 87 which are divisible by 3).
Step 1: Identify the range
We need to find all prime numbers strictly between 60 and 90. That is, integers p such that 60<p<90.
60<p<90
Step 2: List prime numbers in the range
Checking the odd numbers between 60 and 90, the prime numbers are: 61, 67, 71, 73, 79, 83, and 89.
p∈{61,67,71,73,79,83,89}
Step 3: Calculate the sum of these prime numbers
Summing all the identified prime numbers: 61+67+71+73+79+83+89=523.
61+67+71+73+79+83+89=523
Option C is correct because the sum of all prime numbers between 60 and 90 is 523.
Always verify primality using divisibility tests up to n for numbers in higher ranges.
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