Twin Primes Quiz: Testing And Applications

1) Twin primes always differ by 2.

True

False

Twin primes are pairs of prime numbers that differ by 2. Example: (3,5),(11,13). By definition, the difference is exactly 2.

Explanation

Twin primes are pairs of prime numbers that differ by 2. Example: (3,5),(11,13). By definition, the difference is exactly 2.

2) All twin prime pairs include the number 2.

True

False

Only (2,3) includes 2 but diff=1, not 2. (3,5) is first true twin prime. Hence false.

Explanation

Only (2,3) includes 2 but diff=1, not 2. (3,5) is first true twin prime. Hence false.

3) If n is odd and prime, then n+2 is always prime.

True

False

Example:7 prime,7+2=9=3×3 not prime. Hence false.

Explanation

Example:7 prime,7+2=9=3×3 not prime. Hence false.

4) What is the next twin prime pair after (17,19)?

(19,21)

(29,31)

(21,23)

(41,43)

After (17,19), next primes 23,29,31→29+2=31→both prime→(29,31).

Explanation

After (17,19), next primes 23,29,31→29+2=31→both prime→(29,31).

5) Complete the twin prime pair:(__,73) where both are prime.

73−2=71, check divisibility by 2,3,5,7 none divide→prime→pair(71,73).

Explanation

73−2=71, check divisibility by 2,3,5,7 none divide→prime→pair(71,73).

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6) There are no twin primes greater than 100.

True

False

Examples:(101,103),(107,109),(191,193). Twin primes exist beyond 100. False.

Explanation

Examples:(101,103),(107,109),(191,193). Twin primes exist beyond 100. False.

7) Every even number greater than 2 can be part of a twin prime pair.

True

False

Even numbers>2 not prime→cannot be in twin prime pair.

Explanation

Even numbers>2 not prime→cannot be in twin prime pair.

8) Which of the following is a twin prime pair?

(7,11)

(11,13)

(17,21)

(29,31)

A)7 and 11 differ by 4→not twin. B)11,13 both prime, diff=2→twin. C)21 not prime. D)29,31 both prime, diff=2→twin.

Explanation

A)7 and 11 differ by 4→not twin. B)11,13 both prime, diff=2→twin. C)21 not prime. D)29,31 both prime, diff=2→twin.

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9) Which of these numbers could be the smaller number in a twin prime pair?

3

8

17

41

3→3+2=5→both prime. 8 not prime. 17→19 both prime. 41→43 both prime.

Explanation

3→3+2=5→both prime. 8 not prime. 17→19 both prime. 41→43 both prime.

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10) How many twin prime pairs are there between 1 and 20?

3

4

5

6

Primes≤20:2,3,5,7,11,13,17,19→Twin pairs:(3,5),(5,7),(11,13),(17,19)=4 pairs.

Explanation

Primes≤20:2,3,5,7,11,13,17,19→Twin pairs:(3,5),(5,7),(11,13),(17,19)=4 pairs.

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12) Select all twin prime pairs:

(2,3)

(3,5)

(7,9)

-101,103

(2,3) diff=1 not twin. (3,5) yes. (7,9) no 9=3×3. (101,103) both prime diff=2 yes.

Explanation

(2,3) diff=1 not twin. (3,5) yes. (7,9) no 9=3×3. (101,103) both prime diff=2 yes.

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13) Which number cannot be part of a twin prime pair?

5

15

17

59

5→(3,5),(5,7). 15=3×5 not prime→cannot be in twin prime pair. 17,59 both have pairs.

Explanation

5→(3,5),(5,7). 15=3×5 not prime→cannot be in twin prime pair. 17,59 both have pairs.

14) Which of these are twin primes?

(43,45)

(59,61)

(71,73)

-101,103

45 not prime, others all twin primes diff=2.

Explanation

45 not prime, others all twin primes diff=2.

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16) How many numbers between 1 and 30 must you check to find all twin prime pairs?

15

30

14

28

Twin primes>2 are odd. Odd numbers 3–29: count=(29−3)/2+1=15.

Explanation

Twin primes>2 are odd. Odd numbers 3–29: count=(29−3)/2+1=15.

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18) Which twin prime pair has a sum of 24?

(5,7)

(11,13)

(17,19)

(7,17)

(11,13):11+13=24 others differ. (7,17) diff=10 not twin.

Explanation

(11,13):11+13=24 others differ. (7,17) diff=10 not twin.

19) Select all true statements about twin primes:

They always differ by 2.

One of them is always even.

(3,5) is the smallest twin prime pair.

There are infinitely many twin primes (proven).

Differ by 2→true. One even→false. (3,5)→smallest→true. Infinite→conjecture not proven.

Explanation

Differ by 2→true. One even→false. (3,5)→smallest→true. Infinite→conjecture not proven.

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20) The twin prime pair that comes after (5,7) is (,).

List primes:2,3,5,7,11,13,… After (5,7), next pair differing by 2 is (11,13).

Explanation

List primes:2,3,5,7,11,13,… After (5,7), next pair differing by 2 is (11,13).

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Twin Primes Quiz: Testing and Applications

1) Twin primes always differ by 2.

2) All twin prime pairs include the number 2.

3) If n is odd and prime, then n+2 is always prime.

4) What is the next twin prime pair after (17,19)?

5) Complete the twin prime pair:(__,73) where both are prime.

6) There are no twin primes greater than 100.

7) Every even number greater than 2 can be part of a twin prime pair.

8) Which of the following is a twin prime pair?

9) Which of these numbers could be the smaller number in a twin prime pair?

10) How many twin prime pairs are there between 1 and 20?

11) The largest twin prime pair less than 50 is (,).

12) Select all twin prime pairs:

13) Which number cannot be part of a twin prime pair?

14) Which of these are twin primes?

15) The twin prime pair with the smallest sum is (,).

16) How many numbers between 1 and 30 must you check to find all twin prime pairs?

17) The missing number in the twin prime pair (,47) is .

18) Which twin prime pair has a sum of 24?

19) Select all true statements about twin primes:

20) The twin prime pair that comes after (5,7) is (,).

Twin Primes Quiz: Testing and Applications

1) Twin primes always differ by 2.

2) All twin prime pairs include the number 2.

3) If n is odd and prime, then n+2 is always prime.

4) What is the next twin prime pair after (17,19)?

5) Complete the twin prime pair:(__,73) where both are prime.

6) There are no twin primes greater than 100.

7) Every even number greater than 2 can be part of a twin prime pair.

8) Which of the following is a twin prime pair?

9) Which of these numbers could be the smaller number in a twin prime pair?

10) How many twin prime pairs are there between 1 and 20?

11) The largest twin prime pair less than 50 is (__,__).

12) Select all twin prime pairs:

13) Which number cannot be part of a twin prime pair?

14) Which of these are twin primes?

15) The twin prime pair with the smallest sum is (__,__).

16) How many numbers between 1 and 30 must you check to find all twin prime pairs?

17) The missing number in the twin prime pair (__,47) is __.

18) Which twin prime pair has a sum of 24?

19) Select all true statements about twin primes:

20) The twin prime pair that comes after (5,7) is (__,__).

11) The largest twin prime pair less than 50 is (,).

15) The twin prime pair with the smallest sum is (,).

17) The missing number in the twin prime pair (,47) is .

20) The twin prime pair that comes after (5,7) is (,).