Patterns with the Sieve

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Reviewed by Cierra Henderson
Cierra Henderson, MBA |
K-12 Expert
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Quizzes Created: 8156 | Total Attempts: 9,588,805
| Attempts: 12 | Questions: 20 | Updated: Jan 19, 2026
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Question 1 / 20
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1) What pattern do prime numbers follow in the sieve?

Explanation

Primes are the numbers that remain uncrossed.

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About This Quiz
Patterns With The Sieve - Quiz

Think you can predict which numbers will survive the sieve? In this quiz, you’ll uncover patterns in prime numbers—seeing which ones stay, which ones vanish, and how primes pop up in different ranges. By the end, you’ll discover how the sieve makes prime patterns clear as day.

2) Which prime numbers appear between 50 and 60?

Explanation

The primes between 50 and 60 are 53 and 59.

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3) What is the 10th prime number in the sieve?

Explanation

The 10th prime number in the sieve is 29.

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4) Which number is eliminated when crossing out multiples of 13 up to 100?

Explanation

Multiples of 13 like 39 and 52 are eliminated.

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5) Which number pattern matches multiples of 2?

Explanation

Multiples of 2 follow the pattern 2, 4, 6, 8, and so on.

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6) Which prime comes directly before 50?

Explanation

The prime directly before 50 is 47.

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7) Which prime is between 70 and 80?

Explanation

The prime between 70 and 80 is 73.

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8) Which number is composite?

Explanation

The number 63 is composite because 63 = 7 × 9.

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9) Which prime factorization is correct for 21?

Explanation

The prime factorization of 21 is 3 × 7.

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10) Which prime comes after 89?

Explanation

The prime that comes after 89 is 97.

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11) Which prime numbers are between 90 and 100?

Explanation

The only prime between 90 and 100 is 97.

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12) Which number is prime?

Explanation

The number 89 is prime because it has only two factors.

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13) Which number is eliminated when removing multiples of 17 up to 100?

Explanation

The number 34 is crossed out when removing multiples of 17.

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14) Which prime comes directly after 59?

Explanation

The prime directly after 59 is 61.

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15) Which prime numbers are between 10–20?

Explanation

The primes between 10 and 20 are 11, 13, 17, and 19.

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16) Which prime is just before 30?

Explanation

The prime just before 30 is 29.

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17) Which number gets crossed out when eliminating multiples of 19 up to 100?

Explanation

Multiples of 19 like 38, 57, and 76 all get crossed out.

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18) Which prime number comes after 71? 

Explanation

The prime after 71 is 73.

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19) Which prime numbers are between 30–40? 

Explanation

The primes between 30 and 40 are 31 and 37.

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20) What do the sieve's leftover numbers always represent?

Explanation

The leftover numbers in the sieve are always prime numbers.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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What pattern do prime numbers follow in the sieve?
Which prime numbers appear between 50 and 60?
What is the 10th prime number in the sieve?
Which number is eliminated when crossing out multiples of 13 up to...
Which number pattern matches multiples of 2?
Which prime comes directly before 50?
Which prime is between 70 and 80?
Which number is composite?
Which prime factorization is correct for 21?
Which prime comes after 89?
Which prime numbers are between 90 and 100?
Which number is prime?
Which number is eliminated when removing multiples of 17 up to 100?
Which prime comes directly after 59?
Which prime numbers are between 10–20?
Which prime is just before 30?
Which number gets crossed out when eliminating multiples of 19 up to...
Which prime number comes after 71? 
Which prime numbers are between 30–40? 
What do the sieve's leftover numbers always represent?
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