It is 7 because as the product of its prime factors they are: 7*151*223 = 235,711
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The next prime number after 235,711 is 235,723
70
If a number has 5 factors then it most certainly is not prime. Hence there is some confusion as to what you are asking here.
16 if the prime factors don't have to be distinct. 210 if they do.
Prime numbers, raised to a power, have one more factor than their exponents. The smallest prime number is 2. 210 has eleven factors. 210 = 1024