Twin Primes Challenge

1) Which of the following pairs are both prime and differ by 2?

(9,11)

(11,13)

(15,17)

(19,21)

9=3×3 not prime. (11,13) both primes diff=2. (15,17) and (19,21) have composites. So (11,13) is correct.

Explanation

9=3×3 not prime. (11,13) both primes diff=2. (15,17) and (19,21) have composites. So (11,13) is correct.

2) Twin primes are always two prime numbers that differ by 2.

True

False

By definition, twin primes are pairs of prime numbers that differ by 2. Example: (3,5) → 5−3=2; both are prime.

Explanation

By definition, twin primes are pairs of prime numbers that differ by 2. Example: (3,5) → 5−3=2; both are prime.

3) Select all that show twin primes correctly:

(5,7)

(13,15)

(29,31)

(49,51)

(5,7) both primes diff=2. (13,15) and (49,51) have composites. (29,31) both primes diff=2.

Explanation

(5,7) both primes diff=2. (13,15) and (49,51) have composites. (29,31) both primes diff=2.

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4) Every odd prime number is part of a twin prime pair.

True

False

Example: 23 is prime but neither 21 nor 25 is prime → not part of any twin prime pair.

Explanation

Example: 23 is prime but neither 21 nor 25 is prime → not part of any twin prime pair.

5) Which of these pairs is not a twin prime pair?

(17,19)

(29,31)

(41,43)

(43,47)

(43,47) differ by 4 → not twins. The rest differ by 2.

Explanation

(43,47) differ by 4 → not twins. The rest differ by 2.

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7) Twin primes can include an even number.

True

False

2 is only even prime. (2,4) invalid. No twin prime includes even number.

Explanation

2 is only even prime. (2,4) invalid. No twin prime includes even number.

8) What is the sum of the twin primes (11,13)?

22

24

26

28

11+13=24 → correct sum.

Explanation

11+13=24 → correct sum.

9) The pair (101,103) are twin primes.

True

False

Both 101 and 103 are primes, diff=2 → valid twin prime pair.

Explanation

Both 101 and 103 are primes, diff=2 → valid twin prime pair.

10) The twin prime pair (5,7) has a sum smaller than (11,13).

True

False

5+7=12 < 24=11+13 → statement true.

Explanation

5+7=12 < 24=11+13 → statement true.

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12) There are twin primes between 80 and 90.

True

False

Primes in that range: 83,89 → diff=6, not 2 → no twin primes.

Explanation

Primes in that range: 83,89 → diff=6, not 2 → no twin primes.

13) Choose all pairs that are not twin primes.

(7,9)

(17,19)

(23,25)

(41,43)

(7,9) and (23,25) include non-primes. Others are valid twin primes.

Explanation

(7,9) and (23,25) include non-primes. Others are valid twin primes.

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14) Which of these pairs lies between 90 and 110?

(89,91)

(97,99)

-101,103

-111,113

(101,103) both primes → valid twin pair in that range.

Explanation

(101,103) both primes → valid twin pair in that range.

15) Select all true statements about twin primes:

They always differ by 2

There are infinitely many (proven)

(3,5) is the smallest twin prime pair

(2,3) is a twin prime pair

Differ by 2→True. Infinite→Unproven. (3,5) smallest→True. (2,3) diff=1→False.

Explanation

Differ by 2→True. Infinite→Unproven. (3,5) smallest→True. (2,3) diff=1→False.

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16) Which number cannot appear in any twin prime pair?

2

7

23

15

15=3×5 → composite, cannot appear in any twin prime pair.

Explanation

15=3×5 → composite, cannot appear in any twin prime pair.

17) Which pairs are twin primes?

(3,5)

(19,21)

(71,73)

(89,91)

(3,5) and (71,73) both primes diff=2. Others include composites.

Explanation

(3,5) and (71,73) both primes diff=2. Others include composites.

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Twin Primes Challenge

1) Which of the following pairs are both prime and differ by 2?

2) Twin primes are always two prime numbers that differ by 2.

3) Select all that show twin primes correctly:

4) Every odd prime number is part of a twin prime pair.

5) Which of these pairs is not a twin prime pair?

6) Complete the pair: (__,61) → both numbers must be prime.

7) Twin primes can include an even number.

8) What is the sum of the twin primes (11,13)?

9) The pair (101,103) are twin primes.

10) The twin prime pair (5,7) has a sum smaller than (11,13).

11) The missing number in the pair (,19) is .

12) There are twin primes between 80 and 90.

13) Choose all pairs that are not twin primes.

14) Which of these pairs lies between 90 and 110?

15) Select all true statements about twin primes:

16) Which number cannot appear in any twin prime pair?

17) Which pairs are twin primes?

18) The smallest twin prime pair after (29,31) is (,).

19) The twin prime pair immediately before (11,13) is (,).

20) The twin prime pair that comes after (11,13) is (,).

Twin Primes Challenge

1) Which of the following pairs are both prime and differ by 2?

2) Twin primes are always two prime numbers that differ by 2.

3) Select all that show twin primes correctly:

4) Every odd prime number is part of a twin prime pair.

5) Which of these pairs is not a twin prime pair?

6) Complete the pair: (__,61) → both numbers must be prime.

7) Twin primes can include an even number.

8) What is the sum of the twin primes (11,13)?

9) The pair (101,103) are twin primes.

10) The twin prime pair (5,7) has a sum smaller than (11,13).

11) The missing number in the pair (__,19) is __.

12) There are twin primes between 80 and 90.

13) Choose all pairs that are not twin primes.

14) Which of these pairs lies between 90 and 110?

15) Select all true statements about twin primes:

16) Which number cannot appear in any twin prime pair?

17) Which pairs are twin primes?

18) The smallest twin prime pair after (29,31) is (__,__).

19) The twin prime pair immediately before (11,13) is (__,__).

20) The twin prime pair that comes after (11,13) is (__,__).

11) The missing number in the pair (,19) is .

18) The smallest twin prime pair after (29,31) is (,).

19) The twin prime pair immediately before (11,13) is (,).

20) The twin prime pair that comes after (11,13) is (,).