Prime Numbers Between 1 and 100: 58 flashcards
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1. What is a prime number?
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A whole number greater than 1 with exactly two factors: 1 and itself.
2. Is 1 a prime number?
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No. 1 has only one factor, so it is neither prime nor composite.
3. What is the only even prime number?
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2
4. How many prime numbers are there between 1 and 100?
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25
5. List all primes between 1 and 100.
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
6. What is a composite number?
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A whole number greater than 1 that has more than two factors.
7. Which primes must you test to check if a number under 100 is prime?
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2, 3, 5, and 7
8. What is the Sieve of Eratosthenes?
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A systematic method for finding all primes up to a given limit by crossing out multiples of each prime.
9. Is 91 a prime number?
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No. 91 = 7 × 13, so it is composite.
10. Is 87 a prime number?
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No. 87 = 3 × 29, so it is composite.
11. Is 57 a prime number?
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No. 57 = 3 × 19, so it is composite.
12. What are twin primes?
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Pairs of primes that differ by 2, such as (3, 5), (5, 7), (11, 13).
13. What does the Fundamental Theorem of Arithmetic state?
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Every integer greater than 1 has a unique prime factorization.
14. What is π(100) in prime counting?
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25 — the number of primes up to 100.
15. Are all odd numbers prime?
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No. Many odd numbers like 9, 15, 21, 25, 27, 33, 35, 39, 45, 49 are composite.
16. What is the smallest odd composite number?
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9 (since 9 = 3 × 3)
17. Why is 2 the only even prime?
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Every even number greater than 2 has at least three factors: 1, 2, and itself.
18. How many primes are there between 1 and 10?
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4 (2, 3, 5, 7)
19. How many primes are there between 91 and 100?
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1 (only 97)
20. What is the largest prime number below 100?
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97
21. What is the smallest prime number?
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2
22. Is 0 a prime number?
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No. 0 is not prime because it does not have exactly two factors.
23. What is the square root of 100, and why does it matter for prime testing?
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√100 = 10, so you only need to test primes up to 10 (2, 3, 5, 7) to check any number under 100.
24. Give an example of a prime factorization.
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84 = 2² × 3 × 7
25. What is the prime counting function π(n)?
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A function that counts the number of primes less than or equal to n.
26. Name three primes between 50 and 70.
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53, 59, 61, 67 (any three of these)
27. Name three primes between 70 and 90.
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71, 73, 79, 83, 89 (any three of these)
28. Why do primes become less frequent as numbers increase?
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Because larger numbers have more potential divisors, making it harder to have exactly two factors.
29. What is the gap between consecutive twin primes?
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2
30. Is 49 a prime number?
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No. 49 = 7 × 7, so it is composite.
31. Is 77 a prime number?
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No. 77 = 7 × 11, so it is composite.
32. Is 51 a prime number?
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No. 51 = 3 × 17, so it is composite.
33. Is 93 a prime number?
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No. 93 = 3 × 31, so it is composite.
34. What is the smallest prime greater than 50?
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53
35. What is the smallest prime greater than 80?
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83
36. How many primes are there between 1 and 20?
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8 (2, 3, 5, 7, 11, 13, 17, 19)
37. What is the only prime number that is also a perfect square?
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There is none — a perfect square has an odd number of factors, so it cannot have exactly two.
38. Why is the Sieve of Eratosthenes efficient for finding primes up to 100?
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Because you only need to sieve with primes up to √100 = 10, i.e., 2, 3, 5, and 7.
39. What is the density of primes under 100?
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25 out of 100, or 25%.
40. Name a prime between 30 and 40.
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31 or 37
41. Name a prime between 40 and 50.
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41, 43, or 47
42. Is 99 a prime number?
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No. 99 = 9 × 11 = 3² × 11, so it is composite.
43. What is the largest two-digit prime?
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97
44. What is the smallest two-digit prime?
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11
45. How many primes are there between 1 and 50?
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15 (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47)
46. How many primes are there between 50 and 100?
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10 (53, 59, 61, 67, 71, 73, 79, 83, 89, 97)
47. Is 63 a prime number?
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No. 63 = 3 × 21 = 3² × 7, so it is composite.
48. Is 69 a prime number?
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No. 69 = 3 × 23, so it is composite.
49. Is 81 a prime number?
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No. 81 = 9 × 9 = 3⁴, so it is composite.
50. Is 95 a prime number?
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No. 95 = 5 × 19, so it is composite.
51. What is the smallest prime factor of any composite number under 100?
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It must be 2, 3, 5, or 7.
52. Why is 1 not considered prime?
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Because it has only one factor (itself), not exactly two distinct factors.
53. What is the next prime after 89?
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97
54. What is the prime factorization of 100?
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100 = 2² × 5²
55. What is the prime factorization of 72?
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72 = 2³ × 3²
56. What is the prime factorization of 60?
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60 = 2² × 3 × 5
57. What is the prime factorization of 84?
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84 = 2² × 3 × 7
58. What is the prime factorization of 90?
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90 = 2 × 3² × 5
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