Call a positive integer kinda-prime if it has a prime number of positive integer divisors. If there are 168 prime numbers less than 1000, how many kinda-prime positive integers are there less than 1000?

Guest Apr 11, 2021

#1**0 **

https://web2.0calc.com/questions/help-with-permutations_1

It's answered already. :)))

=^._.^=

catmg Apr 11, 2021

#3**0 **

Hmm, I shall try my best to solve. :))

So, we need our numbers to be in the form of a^b where a is a prime number, and b is one less than a prime number.

If a = 2, then b can be 1, 2, 4, 6. (4 options)

If a = 3, then b can be 1, 2, 4, 6. (4 options)

If a = 5, then b can be 1, 2, 4. (3 options)

If a = 7, then b can be 1, 2. (2 optinos)

If a = 11, then be can be 1, 2. (2 options)

From there, any a from 11 - 31 will have 2 options for b (1, 2).

4+4+3+21*2 = 53.

Someone please check this, I'm really not confident, but I hope this helped.

=^._.^=

catmg
Apr 11, 2021