Identifying Twin Primes

1) The numbers 71 and 73 are:

Composite numbers

Twin primes

Consecutive even numbers

Multiples of 5

They are both prime and differ by 2.

Explanation

They are both prime and differ by 2.

2) Which number pair is not twin primes?

3 and 5

5 and 7

11 and 13

14 and 16

Twin primes are pairs of prime numbers that have a difference of two. In this case, the pair 14 and 16 is not prime, as 14 is divisible by 2 and 16 is divisible by 2 as well, thus they cannot be considered twin primes.

Explanation

Twin primes are pairs of prime numbers that have a difference of two. In this case, the pair 14 and 16 is not prime, as 14 is divisible by 2 and 16 is divisible by 2 as well, thus they cannot be considered twin primes.

3) Which set shows twin primes correctly?

{7, 9}

{13, 15}

{11, 13}

{21, 23}

Both are prime and differ by 2. The others include non-primes.

Explanation

Both are prime and differ by 2. The others include non-primes.

4) The twin prime pair closest to 20 is:

19 and 21

17 and 19

15 and 17

21 and 23

Twin primes are pairs of prime numbers that have a difference of two. The pair 17 and 19 is the closest twin prime pair to 20, as both numbers are prime and their difference is exactly 2.

Explanation

Twin primes are pairs of prime numbers that have a difference of two. The pair 17 and 19 is the closest twin prime pair to 20, as both numbers are prime and their difference is exactly 2.

5) Which of these numbers does not belong to a twin prime pair?

3

5

7

9

9 is not prime. The others all belong to valid twin pairs.

Explanation

9 is not prime. The others all belong to valid twin pairs.

6) Which is the largest twin prime pair under 20?

7 and 9

17 and 19

11 and 12

13 and 14

This is the final twin pair before 20.

Explanation

This is the final twin pair before 20.

7) Which of these pairs is not both prime?

3 and 5

5 and 7

9 and 11

11 and 13

9 is not prime. All other pairs are twin primes.

Explanation

9 is not prime. All other pairs are twin primes.

8) What is the difference between any two twin primes?

1

2

4

3

By definition, twin primes always differ by 2.

Explanation

By definition, twin primes always differ by 2.

9) Which is the smallest twin prime pair?

1 and 3

3 and 5

5 and 7

7 and 9

The first twin primes are 3 and 5.

Explanation

The first twin primes are 3 and 5.

10) Which twin primes straddle 60?

51 and 53

59 and 61

55 and 57

57 and 59

Both are primes just below and above 60.

Explanation

Both are primes just below and above 60.

11) Which prime pair is separated by 4 instead of 2?

3 and 5

11 and 13

17 and 19

13 and 17

These are both primes but not twin primes, since the difference is 4.

Explanation

These are both primes but not twin primes, since the difference is 4.

12) Which number completes the twin prime pair with 59?

57

61

63

65

59 and 61 are twin primes.

Explanation

59 and 61 are twin primes.

13) Which pair is both prime and consecutive odd numbers?

15 and 17

17 and 19

29 and 33

33 and 35

They are consecutive odd primes differing by 2.

Explanation

They are consecutive odd primes differing by 2.

14) Which number belongs to a twin prime pair?

35

45

55

41

41 is prime and pairs with 43.

Explanation

41 is prime and pairs with 43.

15) Which pair is a set of twin primes?

31 and 32

41 and 43

49 and 51

51 and 53

Both are primes and 2 apart. Other options include non-primes.

Explanation

Both are primes and 2 apart. Other options include non-primes.

16) Which number is prime but not part of a twin prime pair?

23

29

31

41

23 is prime, but neither 21 nor 25 is prime, so it has no twin.

Explanation

23 is prime, but neither 21 nor 25 is prime, so it has no twin.

17) Which of these is not a twin prime pair?

41 and 43

29 and 31

11 and 13

21 and 23

21 is not prime.

Explanation

21 is not prime.

18) Which number is part of a twin prime pair?

20

21

29

35

29 is prime and pairs with 31. 20, 21, and 35 are not prime.

Explanation

29 is prime and pairs with 31. 20, 21, and 35 are not prime.

19) Which of the following is a pair of twin primes?

9 and 11

11 and 13

17 and 19

21 and 23

Twin primes are pairs of prime numbers that have a difference of two. In this case, 17 and 19 are both prime and their difference is 2, making them a pair of twin primes.

Explanation

Twin primes are pairs of prime numbers that have a difference of two. In this case, 17 and 19 are both prime and their difference is 2, making them a pair of twin primes.

20) Which number begins the next twin prime pair after 31?

33

37

39

41

The pair is 37 and 39, but since 39 is not prime, the next true twin pair is actually 41 & 43. So the best correct option from given choices is 37 (leading to the next prime check).

Explanation

The pair is 37 and 39, but since 39 is not prime, the next true twin pair is actually 41 & 43. So the best correct option from given choices is 37 (leading to the next prime check).