my number is less than 100 one more than a multiple of 3 one of its digits is prime if you reverse its digits you get a prime it has exactly four factors the sum of digits is prime if you miltiply it by 5 it is greater than 100

the last sentence says 21 <= n <= 99

one digit prime and n=3k+1 means we have something in

25,34,43,52,58,61,67,70,76,79,85,91,94

reverse digits is prime means we have

34,67,91

sum of digits is prime means

34,67

four factors leaves
34, which has factors 1,2,17,34

am a factor of 36 and a multiple of 4 i am not a prime number i am not a factor of 50 what number am i

To find the number that satisfies all the given conditions, we can break down the problem step by step:

1. The number is less than 100 and one more than a multiple of 3.
- We know that the number is less than 100, so we start with the smallest multiple of 3 that is greater than 100, which is 102.
- We iterate by adding 3 to subsequent multiples (105, 108, 111, ...) until we find a number that is also less than 100.
- The first number that satisfies both conditions is 105.

2. One of its digits is prime.
- The available prime digits are 2, 3, 5, and 7.
- In 105, the digit 5 is prime, so this condition is satisfied.

3. Reversing the digits gives a prime number.
- Reversing the digits of 105 gives us 501.
- To check if 501 is a prime number, we can divide it by primes up to its square root (in this case, √501 ≈ 22.39).
- We find that 501 is divisible by 3 (167 × 3 = 501), so it is not a prime number.
- Since this condition is not satisfied, the number 105 does not meet all the given conditions.

4. It has exactly four factors.
- A number with exactly four factors is a square of a prime number.
- Since 105 does not satisfy the previous condition, we proceed to the next multiple of 3, which is 108.
- Checking if 108 is a square of a prime number, we find that it is not.
- We continue checking subsequent multiples until we find a square of a prime number.

5. The sum of the digits is prime.
- Proceeding with the next multiple of 3, which is 111.
- Summing up the digits: 1 + 1 + 1 = 3.
- We check if 3 is prime, and it is indeed a prime number.

6. Multiplying by 5 gives a number greater than 100.
- We calculate: 111 × 5 = 555.
- Since 555 is greater than 100, this condition is satisfied.

Putting it all together, we find that the number that satisfies all the given conditions is 111.