In any large range of numbers, more so the higher and larger the range is, there will be more composites than primes. It is far more likely that a given number will be divisible by some number less than the number itself, the higher you go.
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The largest integer that is not the product of two or more different primes would be the largest prime number. Because there are an infinite number of prime numbers, there is no largest integer that is not the product of two or more different primes.
301
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101
20 as a product of primes = 2 * 2 * 5