Quiz about Prime Numbers
Quiz about Prime Numbers

Prime Numbers Trivia Quiz


Many great mathematicians are fascinated by prime numbers. How much do you know about them? Have fun and thanks for playing.

A multiple-choice quiz by Matthew_07. Estimated time: 5 mins.
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Author
Matthew_07
Time
5 mins
Type
Multiple Choice
Quiz #
265,718
Updated
Dec 03 21
# Qns
10
Difficulty
Tough
Avg Score
6 / 10
Plays
1791
Awards
Top 35% Quiz
Last 3 plays: poetkah (8/10), turaguy (7/10), TopherChris (8/10).
1. A prime number is a natural number which can be divided by two different divisors (namely 1 and the prime number itself) without remainders. Which of the followings is/are prime number(s)? Hint

1
Both
Neither
0

2. Which of the following is the greatest 3-digit prime? Hint

996
999
997
998

3. An integer that is greater or equal to 2 is categorized into 2 groups. The first group is the prime number. These prime numbers are the basic building blocks for the second group of number, which is known as? Hint

The composite number
The rational number
The complex number
The irrational number

4. Which of the following statements is false? Hint

An even integer is definitely not a prime number.
Any integer greater than 5 that ends with a 5 is not a prime number.
An odd integer may be a prime number.
In the set of integers from 1 to 1000000, there are more composite numbers than prime numbers.

5. The Sieve of Eratosthenes is one of the methods to determine whether a given integer is a prime number or not. There exists another method, which is called? Hint

The Sieve of Leibniz
The Sieve of Gauss
The Sieve of Fermat
The Sieve of Atkin

6. Many great mathematicians proved that there is an infinite number of prime numbers. Which of the followings is NOT one of them? Hint

Isaac Newton
Euler
Euclid
Harry Furstenberg

7. Any prime number that can be expressed in the form of 2^(2^n) + 1 is called a Fermat prime. On the other hand, what is the name given to a prime number that can be expressed in the form of 2^n - 1, where n is any prime number? Hint

A Mersenne prime
A Wilson prime
A Sophie Germain Prime
A Wagstaff prime

8. The largest known prime number so far (July 2007) is 2^32582657 - 1, which contains approximately 9.8 million digits. Which organization is offering a USD 100,000 reward to the person or group who discovers a prime number which has more than 10 million digits? Hint

Great Internet Mersenne Prime Search
Electronic Frontier Foundation
Electronic Mersenne Foundation
Great Internet Frontier Prime Search

9. A very famous theorem can be used to estimate how many prime numbers are there between 1 and x by using the formula x/In x. Which theorem is it? Hint

The Dirichlet Theorem
The Prime Number Theorem
The Fermat Theorem
The Proth Theorem

10. Prime numbers are used in cryptography algorithms, which are used in the field of military and banking.

True
False


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Quiz Answer Key and Fun Facts
1. A prime number is a natural number which can be divided by two different divisors (namely 1 and the prime number itself) without remainders. Which of the followings is/are prime number(s)?

Answer: Neither

Both 0 and 1 are not prime numbers. 0 is not considered as a prime number because 0 is not a natural number (counting number) itself, as natural numbers begin with 1. On the other hand, 1 is not a not a prime number because the number 1 only has 1 factor. The first few prime numbers are 2, 3, 5, 7, 11, 13...
2. Which of the following is the greatest 3-digit prime?

Answer: 997

Any even integer greater than 2 is not a prime number, so this cross out 996 and 998. If you add up all the numbers in an integer and find that it can be divided by 3, then that integer is a multiple of 3 and hence it is not a prime number. So, 999 is also not a prime number.

Therefore, the answer we are looking for in this question is 997. The greatest 3-digit prime is 997. This follows by 991 and 983.
3. An integer that is greater or equal to 2 is categorized into 2 groups. The first group is the prime number. These prime numbers are the basic building blocks for the second group of number, which is known as?

Answer: The composite number

All non-prime integers that are greater or equal to 2 are composite numbers. Prime numbers are the building blocks for composite numbers, since a composite number can be expressed as a product of 2 or more prime numbers. For example, the number 100 can be expressed as 2x2x5x5. Notice that both 2 and 5 are prime numbers.
4. Which of the following statements is false?

Answer: An even integer is definitely not a prime number.

The first prime number is 2, which is also the only even prime number. Therefore, any even number that is greater than 2 is definitely not a prime number, because it can be divided by 2.
5. The Sieve of Eratosthenes is one of the methods to determine whether a given integer is a prime number or not. There exists another method, which is called?

Answer: The Sieve of Atkin

Both methods can be applied and used to create programming algorithms and the computer will do the rest of the job for you. The Sieve of Eratosthenes is a simple way. Let say you want to find out which numbers (from 1 to 100) are prime numbers. So, first of all you need to list all the 100 numbers down. Then, you start crossing out numbers that are not prime numbers.

First and foremost, 1 is crossed out because it is not a prime number. Next, 2 is circled since it is the smallest and the only even prime number. Cancel out any other even numbers because they are all multiples of 2. This will leave you with less numbers. Next, circle 3 and cross out any other numbers that are multiples of 3. The same routine is used and continued for the rest of the numbers until 100 and you will all the prime numbers you need.

Meanwhile, the Sieve of Atkin is a newer and faster way. It is revised from the Sieve of Eratosthenes. The Sieve of Atkin is used generally in an algoritm, because it is very tedious and troublesome to work out the list manually.
6. Many great mathematicians proved that there is an infinite number of prime numbers. Which of the followings is NOT one of them?

Answer: Isaac Newton

The earliest poof was given by Euclid in his book "Elements". Apart from that, Euler showed that the sum of the reciprocals of all prime numbers is divergent, so this supported the fact that there is an infinite number of prime numbers. Moreover, by using general topology method, Harry Furstenberg also proved this statement.

Another method of proving this is by using mathematical induction method.
7. Any prime number that can be expressed in the form of 2^(2^n) + 1 is called a Fermat prime. On the other hand, what is the name given to a prime number that can be expressed in the form of 2^n - 1, where n is any prime number?

Answer: A Mersenne prime

It is named after a French monk, Marin Mersenne. On 4 September 2006, Dr. Curtis Cooper and his partner, Dr. Steven Boone of Central Missouri State University (CMSU) have found the largest prime number known currently. This prime number, 2^32582657 - 1 is also a Mersenne prime (44th Mersenne prime).

It has as many as 9808358 digits! The 43rd Mersenne prime, which contains 9152052 digits, was also discovered by the pair on 15 December 2005.
8. The largest known prime number so far (July 2007) is 2^32582657 - 1, which contains approximately 9.8 million digits. Which organization is offering a USD 100,000 reward to the person or group who discovers a prime number which has more than 10 million digits?

Answer: Electronic Frontier Foundation

In 2000, the Electronic Frontier Foundation (EFF) gave USD 50,000 for a 1 million digit prime. There are also other awards, including USD 150,000 (for finding a prime number that has more than 100 million digits) and USD 250,000 (for finding a prime number that has more than 1 billion digits).
9. A very famous theorem can be used to estimate how many prime numbers are there between 1 and x by using the formula x/In x. Which theorem is it?

Answer: The Prime Number Theorem

For example, you want to know how many prime numbers are there from 1 to 10. In order to do so, you divide 10 by In 10 to get 4.32, which is close to 4. Indeed, there are 4 prime numbers (2,3,5,7) from 1 to 10.
10. Prime numbers are used in cryptography algorithms, which are used in the field of military and banking.

Answer: True

Prime numbers are used widely in rotor machines. They are used as some kind of "passwords" to protect some very important details.
Source: Author Matthew_07

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This quiz is part of series Fun with Numbers:

A collection of my mathematics quizzes, covering different types of numbers with interesting properties. This list includes composite numbers, consecutive numbers, Fibonacci numbers, palindromic numbers, perfect numbers, prime numbers, square numbers, and triangular numbers.

  1. Composite Numbers Average
  2. Consecutive Numbers Average
  3. Fibonacci Numbers Average
  4. Palindromic Numbers Average
  5. Perfect Numbers Average
  6. Prime Numbers Tough
  7. Square Numbers Average
  8. Triangular Numbers Average

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