The sum of all the prime numbers from 1 to 20 is

### Concept & Logic This requires listing all prime numbers within a defined boundary ($1$ to $20$) and calculating their sum. Accuracy in identifying primes is critical here. ### Step-by-Step Solution First, list all the prime numbers between $1$ and $20$. The primes are: $2, 3, 5, 7, 11, 13, 17$, and $19$. Next, calculate the total sum. To do this efficiently, group the numbers into pairs that end in round numbers: * Pair 1: $11 + 19 = 30$ * Pair 2: $13 + 17 = 30$ * Remaining primes: $2 + 3 + 5 + 7 = 17$ Add the grouped sums together: $$Sum = 30 + 30 + 17$$ $$Sum = 77$$ ### Exam Strategy & Shortcut Do not add the numbers sequentially ($2+3=5, 5+5=10...$) as this increases cognitive load and the chance of a minor arithmetic error under time pressure. Always look for pairs that sum to multiples of $10$ (like the $13+17$ trick shown above) to optimize your calculation speed. ### Common Pitfall Accidentally including $9$ or $15$ in the sum. Because they are odd numbers, students rushing through the exam often mistakenly categorize them as primes. $9$ ($3 \times 3$) and $15$ ($3 \times 5$) are composite. Including $9$ would incorrectly lead to a sum of $86$. ### Final Answer Therefore, the correct answer is 77.