False. An enormous number of them are divisible by three.
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There are an infinite amount of prime numbers that are greater than 100. The first three of those are 101, 103 and 107.
False. 2 x 5 = 10
The premise of your questions is false: NOT every number is a prime number.
Numbers that have only two factors are prime numbers. You're looking for the next three prime numbers over a certain number. But, you didn't tell us what number the three numbers have to be greater than.
23, 29, 31.