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 ( + 1) is also a prime number.

Which of the above statements is/are correct?

Only 1

Only 2

Both 1 and 2

Neither 1 nor 2

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Explanation:

Statement 1

Yes, there exists only one prime number p such that (17p + 1) is a square.
Let p = 19
⇒ (17 × 19 + 1) = 324 which is square of 18, so it is true.
Statement 2
Product of first 10 consecutive numbers $x$ (2, 3, 5, 7, 11, 13, 17, 19, 23, 29) = 6469693230
∴ $x$ + 1 = 6469693231
Divisibility by 7: The difference of the numbers upto thousands place and remaining part of the number if it is divisible by 7 then the number is divisible by 7

Difference = 6469693 – 231 = 6469462