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.

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3) 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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5) 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.

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7) 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.

8) 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.

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10) 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.

11) 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.

12) 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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14) 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.

15) 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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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 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.

18) 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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19) 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.

20) 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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Twin Primes Challenge

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

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

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

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

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

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

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

8) Twin primes can include an even number.

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

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

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

12) Select all that show twin primes correctly:

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

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

15) Which pairs are twin primes?

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

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

18) Choose all pairs that are not twin primes.

19) There are twin primes between 80 and 90.

20) Select all true statements about twin primes:

Twin Primes Challenge

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

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

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

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

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

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

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

8) Twin primes can include an even number.

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

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

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

12) Select all that show twin primes correctly:

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

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

15) Which pairs are twin primes?

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

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

18) Choose all pairs that are not twin primes.

19) There are twin primes between 80 and 90.

20) Select all true statements about twin primes:

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

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

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

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