Find all the two digit prime numbers neither of whose digits are prime.
Someone helped me yesterday but I do not understand.
You need a list of all digits which are not prime:
1,4,6,8,9
(Note that 1 is not considered a prime).
From a list of prime number from 1 to 100, find the primes that are made up of one or both of these 5 digits. For example, 11 is a prime number made up of digits (1 and 1) that are not prime.
List of prime numbers less than 100
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
For how many two digit prime numbers is the sum of its digits 8
To find all the two-digit prime numbers whose digits are not prime, we need to follow these steps:
Step 1: Identify the non-prime digits
Start by listing all the prime numbers less than 10. The prime numbers less than 10 are 2, 3, 5, and 7. These are the only prime digits.
Step 2: Generate all possible two-digit numbers
Next, we need to generate all possible two-digit numbers. Since we want to exclude the prime digits, the tens and units digits of the two-digit numbers cannot be 2, 3, 5, or 7. The tens and units digits can range from 0 to 9, so excluding the prime digits, we have six possible digits left: 0, 1, 4, 6, 8, and 9.
Step 3: Combine the non-prime digits
Using these six non-prime digits, we can now generate all possible two-digit numbers by combining them. For example, we can combine 0 with 1 to get 01, or 0 with 4 to get 04. We also need to consider the order of the digits, so combining 0 with 1 is different from combining 1 with 0.
Step 4: Check for prime numbers
Once we have generated all possible two-digit numbers with the non-prime digits, we need to check which of these numbers are prime. To check if a number is prime, we divide it by all the numbers less than its square root. If it is divisible by any of these numbers, then it is not prime. Otherwise, it is prime.
Step 5: List the prime numbers
Finally, we list all the two-digit prime numbers whose digits are not prime, based on the results of our prime number check in Step 4.
Let's go through an example:
Using the digits 0, 1, 4, 6, 8, and 9, we can generate the following two-digit numbers: 04, 06, 08, 09, 14, 16, 18, 19, 40, 41, 46, 48, 49, 60, 61, 64, 68, 69, 80, 81, 84, 86, 89, 90, 91, 94, 96, 98, 99.
By checking each of these numbers for primality, we find that the only two-digit prime numbers whose digits are not prime are 41 and 89.
Therefore, the two-digit prime numbers neither of whose digits are prime are 41 and 89.