I am a prime number between 40 and 50. If you add one to me, the sum of the prime factors of that composite number is 11. What number am I?
The prime numbers between 40 and 50 are 41, 43, and 47. Which one fits the description? Only one of them does.
41 but still don't understand this subject
To find the prime number that meets the given conditions, let's break down the problem into steps:
Step 1: Determine the composite number
We know that by adding one to the prime number, we get a composite number whose prime factors' sum is 11. Let's list the prime factors of this composite number.
Step 2: Find the composite number
Since the prime factors' sum is 11, we can look for composite numbers that have a product of prime numbers whose sum is 11. Let's list the possible combinations.
1 * 11 = 11 (not composite)
1 * 3 * 3 = 9 (the prime factors' sum is 7)
1 * 2 * 2 * 2 * 2 * 2 = 32 (the prime factors' sum is 11)
Step 3: Substitute the composite number into the original equation
We found that the composite number with a prime factors' sum of 11 is 32. Now we need to substitute it back into the original question:
"If you add one to me, the sum of the prime factors of that composite number is 11."
If we add 1 to 32, we get 33. The prime factors of 33 are 3 and 11, which sum up to 14, not 11. Therefore, 32 is not the correct composite number.
Step 4: Find another composite number
Let's look for another composite number with a prime factors' sum of 11.
1 * 5 * 5 = 25 (the prime factors' sum is 11)
Step 5: Substitute the new composite number into the original equation
If we add 1 to 25, we get 26. The prime factors of 26 are 2 and 13, which sum up to 15, not 11. Therefore, 25 is not the correct composite number either.
Step 6: Continue searching
Since none of the previous composite numbers met the requirements, we need to find another one.
1 * 2 * 2 * 2 * 2 = 16 (the prime factors' sum is 7)
Step 7: Substitute the new composite number into the original equation
If we add 1 to 16, we get 17. The prime factors of 17 are only 17 itself, which sums up to 17. Therefore, 16 is not the correct composite number.
Step 8: Final attempt
Let's search for one final composite number.
1 * 2 * 2 * 3 = 12 (the prime factors' sum is 11)
Step 9: Substitute the new composite number into the original equation
If we add 1 to 12, we get 13. The prime factors of 13 are only 13 itself, which sums up to 13. Therefore, 12 is not the correct composite number.
Step 10: Conclusion
After thorough investigation, we found that there are no prime numbers between 40 and 50 that satisfy the given condition of having its composite number's prime factors' sum equal to 11.