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The sum of all the prime numbers between 51 and 100 is:
724
732
683
687
732
Memorize the list of primes between 50 and 100 (53, 59, 61, 67, 71, 73, 79, 83, 89, 97) and sum them in pairs to avoid calculation errors: (53+97)=150, (59+71)=130, (61+79)=140, (67+83)=150, (73+89)=162.
Range: integers from 51 to 100.
S=∑i=1npi
Memorize the list of primes between 50 and 100 (53, 59, 61, 67, 71, 73, 79, 83, 89, 97) and sum them in pairs to avoid calculation errors: (53+97)=150, (59+71)=130, (61+79)=140, (67+83)=150, (73+89)=162.
Including 51 (3×17), 57 (3×19), 87 (3×29), or 91 (7×13) as primes, which are actually composite.
Identify prime numbers
List all prime numbers in the range [51,100] by excluding composite numbers.
P={53,59,61,67,71,73,79,83,89,97}
Sum the prime numbers
Add all identified prime numbers together to find the total sum.
S=53+59+61+67+71+73+79+83+89+97
Calculation
Grouping for easier addition: 53+97=150, 59+71=130, 61+79=140, 67+83=150, 73+89=162. Then 150+130+140+150+162=732.
S=732
B is correct because the sum of all prime numbers between 51 and 100 is exactly 732.
Prime numbers are frequently tested in divisibility rules and HCF/LCM problems; remembering primes up to 100 saves significant time in exam-hall calculations.
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