Final Answer:
No, it is not possible to find a sequence of m−1 consecutive positive integers none of which is prime for any integer m≥2.
Step-by-step explanation:
In order to determine whether it is possible to find a sequence of m−1 consecutive positive integers none of which is prime, we need to consider the properties of prime numbers. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Therefore, if we take any m−1 consecutive positive integers, at least one of them will be divisible by a prime number. This means that it is not possible to find a sequence of m−1 consecutive positive integers none of which is prime.
For example, let’s consider the sequence of 4 consecutive positive integers: 10, 11, 12, and 13. Among these numbers, 11 and 13 are prime. Even if we consider larger sequences, we will always encounter at least one prime number within the consecutive positive integers.
In conclusion, due to the nature of prime numbers and their distribution among positive integers, it is not possible to find a sequence of m−1 consecutive positive integers none of which is prime for any integer m≥2.