Do we know if the number of primes is finite

Q: How many integers between 100 and 400 contain the digot 2?

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Q: are there any even numbers greater than 2 which are prime? why or why not?

A: We will find the solution in the following step

Q: Find the number of ways to put eight different books in five boxes, if no box is allowed to be…

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Q: A four digit number is to be formed from the digits 0, 2, 5, 7, 8. How many numbers can be formed if…

A: 4 ways to fill it (2,5,7,8) 5 ways to fill it (0,2,5,7,8) 5 ways to fill it (0,2,5,7,8) 5 ways to…

Q: t is desired to write a 3-digit number using the numbers 2, 3, 4, 5, 6, 7, 8. If each number is used…

A: Given Information: It is desired to write a 3-digit number using the numbers 2, 3, 4, 5, 6, 7, 8.…

Q: Using the digitd 3, 4, 5, 6, 7, 8, and 9, how many 4-digit numbers can be constructed if the number…

A: Solution: From the given information, the digits are 3, 4, 5, 6, 7, 8 and 9. Here, the numbers with…

Q: Every natural number can be written as the products of prime numbers

A: Prime numbers are the numbers which have only two factors, 1 and the number itself.

Q: Determine the number of natural numbers less than 700 that can be written using the digtits 5,6,7,9?

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Q: Suppose that 43% of people own dogs. If you pick two people at random, what is the both own a dog?…

A: Given, Probabily of a person own a dog is 43 %

Q: How many five​-digit even numbers are possible if the leftmost digit cannot be​ zero?

A: To count the number of 5 digit integers satisfying the given conditions

Q: How many natural numbers that are less or equal to 1000 and that are not multiples of 3, 5, or 7…

A: A number is said to be divisible by other number if on dividing the number  with it given remainder…

Q: Every natural number greater than 1 can be written as the products of prime numbers.

A: Prove that  every natural number greater than 1 can be expressed as product of primes or the number…

Q: How many four-digit odd numbers less than 5000 can be formed using the digits 2, 3, 4, 5, 6, and 9.

A: Given:  Using the digit 2,3,4,5,6 and 9  We need to find how many four digit odd  number be formed…

Q: Precisely discuss why the Number ‘2’ is a prime number

A: Here we have to discuss why the Number ‘2’ is a prime number.

Q: All prime numbers are odd.

A: We have state whether given statement is True or False. We know that  A prime number is a number…

Q: Assume that you select digits from the set {2,3,5,7} to form a number between 20 and 700. (1) How…

A: The given set of digits is 2,3,5,7 and the range of numbers is 20 to 700. There would be 2 digit…

Q: Suppose you have a number of n digits that can be 1, 2, 5, or 6. How many numbers contain one or…

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Q: Determine the smallest integer that can be expressed as a sum of two primes in three different ways

A: Let us have smallest prime numbers  are, 2,3,5,7,11,13 17,19.....

Q: Give two reasons why the set of odd integers under addition is not agroup.

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Q: How many different seven-digit telephone numbers can be formed if the first digit cannot be zero?

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Q: How many integers between 1000 and 9999 inclusive are not divisible by 5?

A: The number of integers from 1 and 9999 which are divisible by 5 is = [9999 ÷ 5] = [1,999.8] = 1999…

Q: The number of 3-digits numbers that can be formed without repetition from the numbers 2.3.5.7 and 8…

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Q: How many integers between 100 and 999 inclusive are multiples of 13?

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Q: Every odd prime number is greater than 2.

A: Given: "Every odd prime number is greater than 2." To find: Statement in the form "If p, then q"…

Q: Show that given any set of 5 natural numbers, there are 3 numbers whose sum is divisible by 3.

A: Let q∈N. Note that, for every q there exists some x∈N and some v∈0,1,2 such that q=3x+v. Now, let…

Q: How many integers in the set {1,2,3,4, ..., 200} is divisible by at least one of the primes 2, 5 and…

A: Just use inclusion-exclusion principle for three sets.

Q: If repetitions are not permitted, from the 6 digits 0, 2, 3, 4, 5, and 8, how many 4- digit number…

A:

Q: How many different 5-digit odd numbers can be formed from 0, 1, 3, 4, 5, 7, and 9 if repetitions are…

A: Given:Total number of digits = 7 (0, 1, 3, 4, 5, 7, and 9 ) The divisibility rule for 5:The number…

Q: 21 and 24 are not relatively prime numbers

A: To find: Whether 21 and 24 are relatively prime numbers or not?

Q: how many four-digit even numbers are possible if the leftmost digit cannot be zero? repitition is…

A: The question is to find how many 4 digits even numbers are possible if the left most digit cannot be…

Q: What is the sum of the first 100 nonnegative integers?

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Q: In how many ways can you write a 5 digit number such that all the digits are even or all the digits…

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Q: How many four-digit even numbers are possible if the leftmost digit cannot be zero? Repetition is…

A: The question is to find how many 4 digits even numbers are possible if the left most digit cannot be…

Q: How many 5-digit license plate numbers can we generate from the numbers, 0, 1, 2, 3, and 4 if it…

A: Given: There are 5digits 0 , 1 , 2 , 3 , 4 We need to count number of  5 digit number plates…

Q: the greatest prime you must consider to test whether 3524 is prime?

A:

Q: How many integers between 100 and 400 contain the digit 2? There are integers between 100 and 400…

A: Numbers between 200 and 299 contains 2 So total integers = 100 Numbers between 120 – 129 contains 2…

Q: How many numbers between 100 and 999 (inclusive) are divisible by neither 4 nor 5?

A:

Q: How many four-digit odd numbers are possible if the leftmost digit cannot be​ zero? There are…

A: From the given information,Sample space = {0,1,2,3,4,5,6,7,8,9}It has been given that the leftmost…

Q: It is desired to write a 3-digit number using the numbers 2, 3, 4, 5, 6, 7, 8. If each number is…

A: If the 3 digited number is greater than 300, then it will start with the numbers 3, 4, 5, 6, 7, 8.…

Q: How many four-digit even numbers are possible if the leftmost digit cannot be​ zero?

A: The question is to find how many 4 digits even numbers are possible if the left most digit cannot be…

Q: The number of primes of the form n³ – 1 is 1) 1 2) 2 3) Infinite

A: To choose correct option

Q: Determine the smallest integer that can be expressed as a sum of two primes in three different ways.

A: The number is 22 and all others smallest integer can not be written as sum of two primes in three…

Q: How to convince someone that the number 10 is not prime.

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Q: What is the first common multiple of 5 and 7 that is even num

A: Multiple of an integer d:For an integer d, if there exists a  such that n = kd, where n and k are…

Q: To use an automated teller machine at a certain​ bank, you must enter a 5​-digit ​code, using the…

A: You can choose 1st digit in 9 ways.  For each of these 9 ways you can choose 2nd digit in 9 ways as…

Q: How many twin primes are there where both primes are less than or equal to 31? Number of twin…

A: Twin prime: If there is only one composite number between two prime numbers, then that two numbers…

Q: Consider 4 digit numbers with each digit from the set {1, 2, 3, 4, 5, 6, 7, 8, 9} .  How many such…

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Q: 2) How many numbers are there between 6000 and 7000 which have exactly one of their digits as 7?

A: Since, we have to find numbers between 6000 and 7000 so the thousand's place must be occupied by 6.…

Q: How many 3-digit numbers can be formed from the prime numbers from 0 to 10 if the repetition of the…

A: We need to find how many 3 - digit numbers can be formed from the prime numbers from  0  to  10  if…

Q: How many three-digit numbers can be formed if only odd numbers are allowed to be re-used?

A: To find three-digit number that can be formed if only odd numbers are allowed to be re-used. Odd…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.