Answer :

Final answer:

To find three consecutive prime numbers that sum up to 173, one must look for prime numbers around that range and test their sums. After testing several combinations, we conclude that the prime numbers 53, 59, and 61 are the solution as they add up to 173.

Explanation:

The question asks us to find three consecutive prime numbers that add up to 173. To solve this, let's start by listing prime numbers around that range using the sequence provided. We will try to find a set of three prime numbers from the list that sum to 173. Remember, prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves.

  • 163 + 5 (the next prime number) is too small, as it only makes 168.
  • Adding the next prime, 167, gives us 170.
  • The next consecutive prime number after 167 is 173 itself, which leads us to 163 + 167 + 173 = 173 + 330. This sum is too high.

Thus, we must look at smaller primes close to the sum we want. We find the following consecutive primes:

  • 157
  • 158, which is not prime
  • 160, which is also not prime
  • 164, also not prime
  • 165, also not prime
  • 167
  • 171-192 are given ranges, so we focus on individual numbers
  • 173
  • 175 and 176, which are not prime

Looking at the prime numbers 167, 173, and the preceding prime number 163, we find our sum:

  • 163 + 167 + 173 = 503, which is not the sum we're seeking.

We will keep trying until we find the primes that add up to 173. Note that one prime number cannot be part of a consecutive series if it equals the sum. Thus, we explore the sequence of prime numbers right before 173.

  • 157 + 163 + 167 = 487 which is too high.
  • 151 + 157 + 163 = 471, still too high.
  • Going smaller, 149 + 151 + 157 = 457, still not the sum we want.
  • Next we try 147 (which is not a prime number).

After trying a few combinations, we succeed with:

  • 53 + 59 + 61 = 173

Thus, the three consecutive prime numbers that add up to 173 are 53, 59, and 61.

Learn more about Consecutive Prime Numbers here:

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