prime numbers reasoning and problem solving

Prime Numbers Questions

The prime numbers questions and answers are provided here for students to understand the concept quickly. Prime Numbers is one of the most basic concepts taught in primary classes. The questions framed are based on the NCERT curriculum. Students can use these questions to take a quick review of the concepts, and become familiar with the topics by practising them. Check your answers against the detailed explanations provided for each question. To learn more about prime numbers, click here .

Go through the below prime numbers questions and answers, and practise them as well.

Prime Numbers Questions with Solutions

1. The smallest prime number is _____.

The smallest prime number is 2 . The number “2” is the only even prime number, which has only two factors, such as 1 and 2.

2. What are the first 10 prime numbers?

The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

3. Is 9 a prime number?

No, the number 9 is not a prime number.

This is because the number 9 has more than 2 factors. The factors of 9 are 1, 3 and 9. Hence, we can consider 9 as a composite number.

Also, read : Composite Numbers .

4. What is the sum of the first 10 prime numbers?

As we know, the first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Therefore, sum = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29.

Hence, the sum of the first ten prime numbers is 129.

5. What is the mean of the first ten prime numbers?

First 10 prime numbers = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

As we know, Mean = Sum of all values / Total number of values

Mean = 129 / 10

Mean = 12.9

Hence, the mean of the first ten prime numbers is 12.9.

6. What is the median of the first ten prime numbers?

As we know,

The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

The prime number sequence is already in ascending order.

So, we have 10 terms here.

Therefore, Median = Mean of 5th and 6th term

Here, 5th term = 11 and 6th term = 13.

Median = (11+13)/2 = 24/2 = 12

Hence, the median of the first ten prime numbers is 12.

7. What is the sum of the first seven prime numbers divided by 2?

We know that the first seven prime numbers are 2, 3, 5, 7, 11, 13, 17.

Therefore, sum = 2+3+5+7+11+13+17 = 58

When the sum is divided by 2, we get

Hence, the sum of the first seven prime numbers divided by 2 is 29.

8. If “p” is the prime number, find the number of factors p 2 has.

As we know, p 2 can be written as the product of p and P. (i.e., p×p). Hence, the factors of p 2 are 1, p and p 2 .

For example, let us take p = 2, the factors of 2 are 1, 2 and 4.

Therefore, p 2 has exactly three factors.

9. Identify the twin primes among the given pair of numbers:

(1, 3), (3, 5), (13, 19), (1, 2)

As know that the number 1 is neither prime nor composite. Hence, we can ignore the pairs (1, 3) and (1, 2).

As we know, twin prime numbers are the pair of prime numbers with a difference of 2.

Here, (3, 5) is a pair of prime numbers with a difference of 2 (i.e) 5 – 3 = 2.

Whereas (13, 19) is also a pair of prime numbers, in which the difference between them is not equal to 2.

Hence, (3, 5) is a twin prime.

Also, read : What are Twin Primes?

10. How many prime numbers are there between 1 and 50?

The list of prime numbers between 1 and 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.

Hence, the number of prime numbers between 1 and 50 is 15.

Video Lesson on Prime Numbers

Practice Questions

• What is the sum of the first 20 prime numbers?
• What is the mean of the first 50 prime numbers?
• If “p” is the prime number, find the number of factors p 3 has.
• Is 15 a prime number?
• Which is the smallest odd prime number?

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Factors, Multiple and Primes - Short Problems

Producing Zeros

Weekly Problem 10 - 2008 If the numbers 1 to 10 are all multiplied together, how many zeros are at the end of the answer?

Factor Trio

Which of the numbers shown is the product of exactly 3 distinct prime factors?

Reversible Primes

How many two-digit primes are there between 10 and 99 which are also prime when reversed?

Multiple Years

Weekly Problem 18 - 2016 The year 2010 is one in which the sum of the digits is a factor of the year itself. What is the next year that has the same property?

Product 100

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The numbers 72, 8, 24, 10, 5, 45, 36, 15 are grouped in pairs so that each pair has the same product. Which number is paired with 10?

Tricky Customer

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Calculation 2000

Weekly Problem 49 - 2013 What is the value of 2000 + 1999 × 2000?

Stamp Collecting

Last week, Tom and Sophie bought some stamps and they spent exactly £10. Can you work out how many stamps they bought?

Prime Order

Weekly Problem 24 - 2006 How many of the rearrangements of the digits 1, 3 and 5 give prime numbers?

Almost a Million

Weekly Problem 26 - 2014 Which of the given numbers is divisible by 6?

Divisible Digits

Can you find the missing digits, given that the number is divisible by 3, 4, 5 and 6?

Little Goldbach

How many of the numbers 1 to 20 are not the sum of two primes?

What's on the Back?

Four cards have a number on one side and a phrase on the back. On each card, the number does not have the property described on the back. What do the four cards have on them?

Multiplication Table Puzzle

In the multiplication table on the right, only some of the numbers have been given. What is the value of A+B+C+D+E?

A whole number less than 100 gives remainders of 2, 3 and 4 when divided by 3, 4 and 5. What is the remainder when it is divided by 7?

Grandma's Cake

What is the smallest number of pieces grandma should cut her cake into to guarantee each grandchild gets the same amount of cake and none is left over?

Cakes and Buns

Helen buys some cakes and some buns for her party. Can you work out how many of each she buys?

Find from Factors

Weekly Problem 35 - 2006 A number has exactly eight factors, two of which are 21 and 35. What is the number?

Jenny's Logic

Weekly Problem 52 - 2009 How did Jenny figure out that Tom's cards added to an even number?

Back of the Queue

Weekly Problem 48 - 2013 What is the remainder when the number 743589×301647 is divided by 5?

Digital Division

How many three digit numbers formed with three different digits from 0, 1, 2, 3 and 5 are divisible by 6?

Smallest Abundant Number

Weekly Problem 34 - 2017 An abundant number is a positive integer N such that the sum of the factors of N is larger than 2N. What is the smallest abundant number?

The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?

Adjacent Factors

Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?

Ones, Twos and Threes

Each digit of a positive integer is 1, 2 or 3, and each of these occurs at least twice. What is the smallest such integer that is not divisible by 2 or 3?

Halloween Day

One year there were exactly four Tuesdays and four Fridays in October. On what day of the week was Halloween.

Red Card Blue Card

Can you arrange the red and blue cards so that the rules are all followed?

Cinema Costs

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Seven from Nine

In how many ways can seven of the numbers 1-9 be chosen such that they add up to a multiple of 3?

Colossal Sum

What is the units digit in this sum of powers of 9?

HCF Expression

Find out which two distinct primes less than $7$ will give the largest highest common factor of these two expressions.

Powerful Finale

Weekly Problem 24 - 2017 What is the last digit of $3^{2011}$?

Given any positive integer n, Paul adds together the factors of n, apart from n itself. Which of the numbers 1, 3, 5, 7 and 9 can never be Paul's answer?

Leap Monday

Can you find the next time that the 29th of February will fall on a Monday?

Missing Digit

What digit must replace the star to make the number a multiple of 11?

Trailing Zeros

How many zeros does 50! have at the end?

Four or Five

The diagram shows a large rectangle composed of 9 smaller rectangles. If each of these rectangles has integer sides, what could the area of the large rectangle be?

Big Blackboard

Can you work out which numbers between 1 and 2016 have exactly two of 2, 3, 4 as factors?

17s and 23s

Can you form this 2010-digit number...

Common Remainder

144 divided by n leaves a remainder of 11. 220 divided by n also leaves a remainder of 11. What is n?

Peter's Primes

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Indivisible

Each time a class lines up in different sized groups, a different number of people are left over. How large can the class be?

Flora the Florist

Flora has roses in three colours. What is the greatest number of identical bunches she can make, using all the flowers?

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End of a Prime

I made a list of every number that is the units digit of at least one prime number. How many digits appear in the list?

Threes and Fours

What is the smallest integer where every digit is a 3 or a 4 and it is divisible by both 3 and 4?

Essential Supplies

Chocolate bars come in boxes of 5 or boxes of 12. How many boxes do you need to have exactly 2005 chocolate bars?

Powerful Zeros

How many zeros are there at the end of $3^4 \times 4^5 \times 5^6$?

Weekly Problem 47 - 2017 How many numbers do I need in a list to have two squares, two primes and two cubes?

Divisible Palindrome

What is the sum of the digits of the largest 4-digit palindromic number which is divisible by 15?

Triangular Algebra

Weekly Problem 26 - 2017 The angles in the triangle are shown in the diagram in terms of x and y. If x and y are positive integers, what is the value of x+y?

Relative Time

Albert Einstein is experimenting with two unusual clocks. At what time do they next agree?

Times and Square

Roger multiplies two consecutive integers and squares the result. Can you find the last two digits of his new number?

Coin Collection

When coins are put into piles of six 3 remain and in piles of eight 7 remain. How many remain when they are put into piles of 24?

Added Power

How many integers $n$ are there for which $n$ and $n^3+3$ are both prime?

Sticky Fingers

Ruth wants to puts stickers on the cuboid she has made from little cubes. Will she have any stickers left over?

Eight Factors Only

We are given two factors of a number with eight factors. Can you work out the other factors of the number?

One of these numbers is the largest of nine consecutive positive integers whose sum is a perfect square. Which one is it?

Last-but-one

What is the last-but-one digit of 99! ?

Primes and Six

Weekly Problem 1 - 2015 If $p$ and $q$ are prime numbers greater than $3$ and $q=p+2$, prove that $pq+1$ is divisible by $36$.

Adding a Square to a Cube

If you take a number and add its square to its cube, how often will you get a perfect square?

Cancelling Fractions

Can you find a fraction with the following properties?

Factor List

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Three Primes

Weekly Problem 6 - 2010 Can you find three primes such that their product is exactly five times their sum? Do you think you have found all possibilities?

Fortunate Inflation

The price of an item in pounds and pence is increased by 4%. The new price is an integer number of pounds. Can you find it?

Weekly Problem 26 - 2008 If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?

Using the hcf and lcf of the numerators, can you deduce which of these fractions are square numbers?

Rational Integer

Weekly Problem 39 - 2012 For how many values of $n$ are both $n$ and $\frac{n+3}{n−1}$ integers?

Factorised Factorial

Weekly Problem 17 - 2010 The value of the factorial $n!$ is written in a different way. Can you work what $n$ must be?

Super Computer

What is the units digit of the given expression?

Square Product

Weekly Problem 10 - 2011 Will this product give a perfect square?

Integer Indices

From this sum of powers, can you find the sum of the indices?

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Prime numbers: Reasoning and Problem Solving

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Prime Numbers - Year 6

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

13 March 2024

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This Year 6 maths teaching resource includes a PowerPoint and differentiated worksheet for independent learning, to guide your class through identifying prime numbers. It will help the children understand how to solve problems involving prime numbers in context, along with deepening their understanding of the four operations, as they will need to use a range of skills including multiplication and division. They will learn to represent prime numbers in a variety of ways, including pictorial representations. The worksheet contains varied fluency, reasoning and problem solving to reinforce and consolidate the children’s learning. The resource supports the White Rose Small Steps guidance, and is designed to support a mastery approach to teaching maths.

Content includes:

‘Prime Numbers - Year 6’ is completely editable giving teachers the freedom to adapt the resource to suit their individual teaching needs.

‘Prime Numbers - Year 6’ is included in our complete teaching unit ‘Factors, Multiples, Primes, Squares and Cubes - Year 6’. Click on the link below to take a closer look.

https://www.tes.com/teaching-resource/factors-multiples-primes-squares-and-cubes-year-6-12158664

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April 3, 2024

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A periodic table of primes: Research team claims that prime numbers can be predicted

by Michael Gibb, City University of Hong Kong

Both arithmetic aficionados and the mathematically challenged will be equally captivated by new research that upends hundreds of years of popular belief about prime numbers.

Contrary to what just about every mathematician on Earth will tell you, prime numbers can be predicted, according to researchers at City University of Hong Kong (CityUHK) and North Carolina State University, U.S.

The research team comprises Han-Lin Li, Shu-Cherng Fang, and Way Kuo. Fang is the Walter Clark Chair Professor of Industrial and Systems Engineering at North Carolina State University. Kuo is a Senior Fellow at the Hong Kong Institute for Advanced Study, CityU.

This is a genuinely revolutionary development in prime number theory, says Way Kuo, who is working on the project alongside researchers from the U.S. The team leader is Han-Lin Li, a Visiting Professor in the Department of Computer Science at CityUHK.

We have known for millennia that an infinite number of prime numbers, i.e., 2, 3, 5, 7, 11, etc., can be divided by themselves and the number 1 only. But until now, we have not been able to predict where the next prime will pop up in a sequence of numbers. In fact, mathematicians have generally agreed that prime numbers are like weeds: they seem just to shoot out randomly.

"But our team has devised a way to predict accurately and swiftly when prime numbers will appear," adds Kuo.

The technical aspects of the research are daunting for all but a handful of mathematicians worldwide. In a nutshell, the outcome of the team's research is a handy periodic table of primes, or the PTP, pointing the locations of prime numbers. The research is available as a working paper in the SSRN Electronic Journal .

The PTP can be used to shed light on finding a future prime, factoring an integer, visualizing an integer and its factors, identifying locations of twin primes, predicting the total number of primes and twin primes or estimating the maximum prime gap within an interval, among others.

More to the point, the PTP has major applications today in areas such as cyber security. Primes are already a fundamental part of encryption and cryptography, so this breakthrough means data can be made much more secure if we can predict prime numbers, Kuo explains.

This advance in prime number research stemmed from working on systems reliability design and a color coding system that uses prime numbers to enable efficient encoding and more effective color compression. During their research, the team discovered that their calculations could be used to predict prime numbers .

Provided by City University of Hong Kong

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Prime Numbers Year 6 Four Operations Resource Pack

Step 11: Prime Numbers Year 6 Resources

Prime Numbers Year 6 Resource Pack includes a teaching PowerPoint and differentiated varied fluency and reasoning and problem solving resources for Autumn Block 2.

Not a member? Sign up here.

What's included in the pack?

This pack includes:

• Prime Numbers Year 6 Teaching PowerPoint.
• Prime Numbers Year 6 Varied Fluency with answers.
• Prime Numbers Year 6 Reasoning and Problem Solving with answers.

National Curriculum Objectives

Mathematics Year 6: (6C5)  Identify common factors, common multiples and prime numbers

Differentiation:

Varied Fluency Developing Questions to support finding prime numbers within 100. Expected Questions to support finding prime numbers within 100 including recognising the sum of two prime numbers and identifying prime factors in numbers up to 50. Greater Depth Questions to support finding prime numbers within 100 including recognising the sum of more than two prime numbers and identifying prime factors in any 2-digit number.

Reasoning and Problem Solving Questions 1, 4 and 7 (Problem Solving) Developing Explain whether a statement involving the sum of two prime numbers, no greater than 100, is correct. Expected Explain whether a statement involving the sum of two pairs of prime numbers, no greater than 100, is correct. Greater Depth Explain whether a statement involving the sum of prime factors for two given numbers is correct.

Questions 2, 5 and 8 (Problem Solving) Developing Combine the digit cards to make prime numbers no greater than 100. Expected Combine the digit cards provided to create two prime numbers, no greater than 100, to make a given number. Greater Depth Combine the digit cards provided to create three prime numbers, no greater than 100, to make number within a given range.

Questions 3, 6 and 9 (Reasoning) Developing Explain which of two statements regarding the position of prime numbers, no greater than 100, is correct. Expected Explain which of two statements regarding the sum of prime numbers, no greater than 100, is correct. Greater Depth Explain which of two statements regarding the prime factors of a given number is correct.

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