What numbers after 100 have only 3 factors?

Question

In math I need to find 5 numbers after 100 that have ONLY 3 factors.

Answer 1

289

Answer 2

Sheesh a feller can't correct his mistake before he gets a thumbs down, yes, you need the square of a prime number for exactly 3 factors.  I realized the product of two non identical primes would yield 4 factors shortly after posting it, my mistake.

The five such lowest numbers, which are greater than 100 are

11²=121; 13²=169; 17² = 289; 19² = 361; 23² = 529

Answer 3

I'm not sure if you mean including themselves or not. If you don't mean that two factors are 1 and themselves, then just multiply three prime numbers together that will give you a number over 100.

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If you really mean ONLY 3 factors, then the only way to get that is if you have 1, some prime factor times itself, and the number.

Therefore, the only numbers with three factors are the squares of primes. For example:

11² = 11·11 = 121

The only factors of 121 are: 1, 11, and 121

I'm sure you can find two more (just make SURE that you square a prime number).