Question

Write any seven pairs of twin primes using 'sieve of Eratosthenes'​

Answer 1

Answer:

It is well-known that using the sieve of Eratosthenes, we can generate the sequence of primes $2,3,5,7,11,13,17,19,, which is known to be infinite. It is a longstanding problem to prove if there are (or there are not) infinitely many twin primes (3,5), (5,7), (11,13), (17,19), (29,31),…

hope it helps you

Answer 2

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Each positive integer has at least two divisors, one and itself. A positive integer is a prime number if it is bigger than 1, and its only divisors are itself and 1. For example, 2, 3, 5, 7, 11, 13, 17, and 19 are prime numbers. Let’s try an ancient way to find the prime numbers between 1 and 100.

In addition to calculating the earth’s circumference and the distances from the earth to the moon and sun, the Greek polymath Eratosthenes (c. 276-c. 194 BCE) devised a method for finding prime numbers. Such numbers, divisible only by 1 and themselves, had intrigued mathematicians for centuries. By inventing his “sieve” to eliminate nonprimes—using a number grid and crossing off multiples of 2, 3, 5, and above—Eratosthenes made prime numbers considerably more accessible.

Each prime number has exactly 2 factors: 1 and the number itself. The Greeks understood the importance of primes as the building blocks of all positive integers. In his Elements, Euclid (about 300 BCE) stated many properties of both composite numbers (integers above one that can be made by multiplying other integers) and primes. These included the fact that every integer can be written as a product of prime numbers, or it is itself prime. A few decades later Eratosthenes developed his method, which can be extended to uncover primes.