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Count primes in a range by listing them

This type of question, asked 3 times: CDS 1 2017, CDS 1 2020, CDS 1 2021. All 3 questions below, oldest first.

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  1. Question 1

    CDS 1 2017

    21
    The number of prime numbers which are less than 100 is

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  2. Question 2

    CDS 1 2020

    8
    If mm is the number of prime numbers between 0 and 50; and nn is the number of prime numbers between 50 and 100, then what is (m−n)(m - n) equal to ?

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  3. Question 3

    CDS 1 2021

    4
    Consider the pairs of prime numbers (m,n)(m, n) between 50 and 100 such that m−n=6m - n = 6. How many such pairs are there?

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