3.3 Prime Number Exercise

What is the sum of all the prime numbers between 80 and 90?

Answer explanation

We can read the primes between 80 and 90 off of the Sieve of Eratosthenes in the text. Or, we can test each odd number between 80 and 90 to see if it’s prime. (The even numbers are obviously not prime.) 81 and 87 are divisible by 3, and 85 is divisible by 5. Both 83 and 89 are prime, and their sum is 172.

Find every number between 70 and 80 that is not prime and is not a multiple of 2, 3, or 5.

What is the largest prime number p such that 8 times p is less than 1000?

How many pairs of primes are there such that sum of the pair is 40?

Answer explanation

If two integers add to 40, then either both are odd or both are even. We don’t have to check the even pairs, since at least one of two even numbers that add to 40 is a composite multiple of 2. So, we check all the pairs of odd numbers that add to 40:

The only sums that consist of two prime numbers are 3+37, 11+29, and 17+23. So, there are 3 pairs of prime numbers that add to 40.

The product of all prime numbers between 1 and 80 is divided by 10. What is the remainder?

Answer explanation

The product of all prime numbers between 1 and 80 includes 2 and 5. Multiplying these gives 10, which means the product of all the primes between 1 and 80 is a multiple of 10. Therefore, the remainder is 0 when this product is divided by 10.

The product of all prime numbers between 1 and 80 is divided by 4. What is the remainder?

How many groups of three prime numbers add to 22? Note: is considered the same group of three primes as .

Answer explanation

Some two-digit prime number remain prime after interchanging the digits. For example, 13 and 31 are both prime.

What is the largest possible sum of a pair of such  numbers?

Answer explanation

It should be number starting with number 9 at the tens digit.
we have 97. and the interchange of it is 79.
So, the sum of both of them are 176