To solve the problem, we can start by listing all the prime numbers less than 900:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Next, we can find all the products of two or more consecutive prime numbers that are less than 900. One way to do this is to first find the smallest set of consecutive primes that multiply to less than 900, then move on to the next set of consecutive primes and so on.
The largest set of consecutive prime numbers that multiply to less than 900 is {2, 3, 5, 7, 11, 13}, which multiplies to 30030. The next set of consecutive primes that multiply to less than 900 is {2, 3, 5, 7, 11}, which multiplies to 2310.
Continuing this process, we find that there are 8 positive integers less than 900 that can be written as a product of two or more consecutive prime numbers. These integers are:
210, 330, 429, 462, 510, 570, 690, and 870.
Therefore, there are 8 positive integers less than 900 that can be written as a product of two or more consecutive prime numbers.