Which of the following are twin primes. a) 841 & 843 b) 857 & 859 c) 701 & 703 d) None of these

Q: ) Compute the smallest prime factor of 2197.

A: We have to Compute the smallest prime factor of 2197.

Q: prove the formula of Mersenne primes

A: A number of the form is a Mersenne prime if and only if p is prime.To prove this we need to show…

Q: 9. using prime factorisation, find the HCF of (i) 2622, 1653 (ii) 1891, 1098 10.Check whether 12"…

A: We have to find out hcf

Q: DOference of twin primes is not divisible by 2. :Select one True False

A: There are infinitely many twin primes, or pairs of primes that differ by 2. For example, 3 and 5, 5…

Q: How many digits does the smallest positive integer K have, while satisfying all of the following…

A: We will construct the number K bu fulfilling the conditions from bottom to top.

Q: Which of the following represents the expression as a single power (104) (107) 10⁹

A:

Q: two consecutive odd numbers are both primes, they are called twin primes. One example of a pair of…

A: A) 19 and 21 : 21 = 7*3 so it's not prime. B) 39 and 41 : 39=13*3 so it's not prime. C) 49 and 51 :…

Q: Exercise 6D Use this Venn diagram to answer Questions 1 and 2. Members of youth club (U) Greg lays…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: highest prime that might need to be checked to find the prime factorization of the number. Then,…

A: We need to determine highest prime that might need to be checked to find prime factorisation.

Q: For which odd primes p is 5 a square mod p?

A:

Q: 1. How many elements are there in Z 2. List all elements in Zis 3. Answer either'true' or "false"…

A:

Q: Identify whether the following problems/questions are deductively/inductively stated.…

A: This is the problem of logical reasoning and the theory of mathematics in general.

Q: 2. Is 1501 a square modulo the prime number 3739? Explain.

A: Step 1: Step 2: Step 3: Step 4:

Q: a)Consider the following data: 3 is a quadratic residue for 23 and 37. 3 is a quadratic nonresidue…

A:

Q: d.) Find the second perfect number using the formula (2P-1)(2P – 1)and the next prime number for P.…

A: As per our guidelines we are supposed to answer only first three subparts of the problem. For the…

Q: 1. Find the canonical prime factorization using Fermat's Method a) 40425 b) 491 2. Find the sum of…

A: 1. To find the canonical prime factorization using Fermat's Method: a. 40425 b. 491 2. To find the…

Q: Find the prime factorization of 224331. List the product of primes in increasing order (in the form…

A:

Q: 1) Prove that the numbers -197, -239 are prime numbers 2) Find all prime numbers between -90 and 90.

A: number system

Q: *) The following number has a missing digit x, n = 13645x04142250 a) If n is divisible by 9, then x…

A:

Q: If p is a prime number greater than 3, which of the following represents the sum of the positive…

A: we will check all the options to ensure which is correct.

Q: 1. For all positive integer n, which of the following expression is divisible by 6? A) 7" – 1 C) 5"…

A:

Q: Find the smallest five consecutive composite integers.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2. What are the prime factors for the below numbers and arrange them in a canonical form. a. 17 b.…

A:

Q: If p and q are twin primes, then which of the following is true. i. p + q is divisible by 3 ii. pq =…

A:

Q: 3. The GCF of any two distinct prime numbers is 1. (Distinct they are not the same number) means

A:

Q: Read the copy of the article titled "A New Proof of Euclid's Theorem" by Filip Saidak, which has…

A: As per the question, we are tasked with examining the article "A New Proof of Euclid's Theorem" by…

Q: 3. In the following, a factor may be prime, composite or 1. Note that 6 has 4 factors (1, 2, 3 and…

A: According to the given information, For part (a) It is required to tell the positive integer with…

Q: describe (a,p)

A: Given, if p is a prime, and a is a positive integer.

Q: 2. For which odd primes p is 11 a

A: If p is a prime, then by Fermat's Little Theorem

Q: For all odd primes p, show that p 2(p-3)!+1.

A:

Q: 11. Use you the test for divisibility and test for primality to find a pair of twin primes between…

A: We want to find the twin prime between 100 to 106 We know that twin prime are the number differ by…

Q: If a, bị c, d are distinct prime numbers with an as smallest prime the a * b * c *d is Prime number…

A: Given: a, b, c, d are distinct prime numbers and  a is the smallest prime number We know that, the…

Q: a) Describe a procedure for finding the prime factorization of an integer.b) Use this procedure to…

A:

Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.