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?
I must be one of:
41
43
47
so add 1
42
44
48
so
42 = 2*3*7 and sum = 11, remarkable
44=2*2*11 nope
48=2*2*2*2*3 nope
So I think 41
41+1=42=2*3*7...2+3+7=12
43+1=44=2*2*11...2+2+11=15
47+1=48=2*2*2*2*3=2+2+2+2+3=11
47 is the answer
To find the prime number in the given range, we can start by checking each number from 40 to 50 to see if it is prime.
Prime numbers are only divisible by 1 and themselves, so we can iterate through the numbers and check if any number has factors other than 1 and itself.
Let's go through each number in the given range to find the prime number:
40 is not a prime number because it is divisible by 2 and 5.
41 is a prime number because it is only divisible by 1 and 41.
42 is not a prime number because it is divisible by 2, 3, 6, 7, 14, and 21.
43 is a prime number because it is only divisible by 1 and 43.
44 is not a prime number because it is divisible by 2, 4, 11, and 22.
45 is not a prime number because it is divisible by 3, 5, 9, and 15.
46 is not a prime number because it is divisible by 2, 23, and 46.
47 is a prime number because it is only divisible by 1 and 47.
48 is not a prime number because it is divisible by 2, 3, 4, 6, 8, 12, 16, and 24.
49 is not a prime number because it is divisible by 7 and 49.
50 is not a prime number because it is divisible by 2, 5, 10, 25, and 50.
Out of the numbers checked, the prime numbers are 41, 43, and 47.
Now, let's add 1 to each of these prime numbers and check their prime factors to find the number whose sum of prime factors is equal to 11.
For 41+1 = 42, the prime factors of 42 are 2, 3, and 7. Their sum is 2 + 3 + 7 = 12, which is not equal to 11.
For 43+1 = 44, the prime factors of 44 are 2 and 11. Their sum is 2 + 11 = 13, which is not equal to 11.
For 47+1 = 48, the prime factors of 48 are 2, 2, 2, and 2. Their sum is 2 + 2 + 2 + 2 = 8, which is not equal to 11.
Therefore, there is no number between 40 and 50 that satisfies the given condition.