The number of prime numbers between 0 and 50 is

### Concept & Logic This relies on direct counting of prime numbers. A prime number is a number greater than $1$ with exactly two divisors. For exam efficiency, the count of primes in standard ranges (like $1-50$ and $50-100$) should be memorized. ### Step-by-Step Solution Let's list all the prime numbers starting from $2$ up to $50$: * Single-digit primes: $2, 3, 5, 7$ (Total: 4) * Teens: $11, 13, 17, 19$ (Total: 4) * Twenties: $23, 29$ (Total: 2) * Thirties: $31, 37$ (Total: 2) * Forties: $41, 43, 47$ (Total: 3) Now, sum the counts: $$4 + 4 + 2 + 2 + 3 = 15$$ There are exactly $15$ prime numbers between $0$ and $50$. ### Exam Strategy & Shortcut Do not calculate this during the exam. Memorize these standard milestones: * Primes between $1$ and $50$: **15** * Primes between $50$ and $100$: **10** * Primes between $1$ and $100$: **25** Knowing this fact instantly saves you a minute of manual calculation and eliminates the risk of missing a number. ### Common Pitfall When manually listing primes, students frequently mistakenly include numbers divisible by $3$ or $7$ that look prime at a glance. Common culprits are $39$ ($3 \times 13$) and $49$ ($7 \times 7$). ### Final Answer Therefore, the correct answer is 15.