2019 · Q7
Which of the following statements is not true?
Elementary MathematicsNumber System
- AThe difference of two prime numbers, both greater than 2, is divisible by 2.
- BFor two different integers m, n and a prime number p, if p divides the product m × n, then p divides either m or n.
- CIf a number is of the form 6n - 1 (n being a natural number), then it is a prime number.
- DThere is only one set of three prime numbers such that there is a gap of 2 between two adjacent prime numbers.
Explanation
A is true: two odd primes differ by an even number. B is true (Euclid's lemma). C is false: e.g. n = 6 gives 6n−1 = 35 = 5×7, which is composite. D is true: among p, p+2, p+4 one is a multiple of 3, so (3, 5, 7) is the only such triple. Hence statement C is the one that is not true.