What is the sum of all prime numbers less than 500 with only 3s and 4s as digits
well, they surely end in 3, so look up a list of primes and add them up.
922
.
To find the sum of all prime numbers with only 3s and 4s as digits less than 500, we can follow these steps:
Step 1: Generate all the possible numbers with only 3s and 4s as digits.
- Start with the smallest number composed of only 3s and 4s, which is 3.
- Incrementally add 1 to each digit in each number starting from the rightmost digit. If a digit reaches 5, change it to 3 and carry over 1 to the next digit.
- Repeat this process until the largest number is obtained, which is 444.
Step 2: Check if each generated number is prime.
- For each generated number, check if it is prime using a primality test such as trial division or the Sieve of Eratosthenes.
- If a number is prime, add it to the running sum.
Step 3: Repeat steps 1 and 2 until all numbers less than 500 have been processed.
Step 4: Calculate the final sum of all the prime numbers generated.
Note: This calculation may be time-consuming due to the potential large number of iterations required, so using an efficient algorithm and computer programming can significantly speed up the process.