Multiple Choice Questions on Consider the following statements 1 There exists only one prime number p such that 17p 1 is a square........... for CDS Exam Preparation

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Multiple Choice Questions

Consider the following statements 1 There exists only one prime number p such that 17p 1 is a square...........

Quantitative Aptitude (CDS) Number System
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    Consider the following statements:

    1. There exists only one prime number p such that (17p + 1) is a square.

    2. If x is the product of 10 consecutive prime numbers starting from 2, then (x + 1) is also a prime number.

    Which of the above statements is/are correct?

    1 only

    Incorrect Answer

    2 only

    Incorrect Answer

    Both 1 and 2

    Correct Answer

    Neither 1 nor 2

    Incorrect Answer
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    Explanation:

    For
    p=17+2=19,17p+1=17×19+1=323+1=324=182

    Hence, statement (1) is correct
    If p1,p2,p3,..,pn are prime numbers, then n=p1p2p3,..,pn+1 is a prime numbers
    x=2×3×5×7×11×13×17×19×23×29
    then
    x+1=2×3×5×7×11×13×17×19×23×29+1

    ,then is also a prime number.

    Hence, statement (2) is correct.

    By: Munesh Kumari
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