Question

let p be a prime number.find the number of prime numbers smaller that 1000 which can be written in the form 2^p^2+1

Answer 1

Answer:

1 prime only (17)

Step-by-step explanation:

Given:

• 2^p^2+1<1000, and p is prime

We know that:

• 2^10=1024

So,

• 2^p^2+1<1000=> p^2<10 => p≤3 => p=3 or p=2- only 2 options for p

• p=3 => p^2=9 => 2^9+1=513 - not a prime number as 5+1+3=9 divisible by 3 and 9

• p=2 => p^2=4 => 2^4+1=17- prime number

As we see there is only 1 solution: 17