Piyush365
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There are no known ‘neat’ expressions that generate only primes! Find counterexamples to the following claims: (i) All numbers of the form 4n² + 1 are prime. (ii) All numbers of the form n² + n + 11 are prime. (iii) All numbers of the form 4ⁿ + 3 are prime.

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Counterexamples disprove all three: for (i), n = 4 gives 4(16) + 1 = 65 = 5 × 13; for (ii), n = 10 gives 121 = 11²; for (iii), n = 3 gives 67? No, n = 2 gives 19, n = 3 gives 67, n = 4 gives 259 = 7 × 37.

Class 9 Ganita Manjari part 2 chapter 9.1 solutions
Class 9 Ganita Manjari Part 2 chapter 9 Page 6 Question Answer

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