what is the largest prime less than 1000? explain how you got ypur answer
http://primes.utm.edu/lists/small/1000.txt
997
To find the largest prime number less than 1000, we can start by listing all the numbers from 2 to 999. We'll check each number to see if it is prime or not.
To determine whether a number is prime, we can use a technique called trial division. We divide the number by all the numbers less than its square root. If the number is divisible by any of these smaller numbers, then it is not prime.
Let's follow this process to find the largest prime number less than 1000:
1. Start with the number 999, since it is the largest number less than 1000.
2. Check if 999 is divisible by any numbers less than its square root. We start with 2 and continue checking until we reach the square root of 999 (which is approximately 31.6).
3. We find that 999 is divisible by 3. Therefore, we know that 999 is not a prime number.
4. Move on to the next number, 998. Repeat the same check. We find that 998 is divisible by 2 and 499, which means it is not prime.
5. Continue this process for the next numbers, all the way down to 2.
6. Finally, we reach the number 997. We check if any numbers less than the square root of 997 divide it, and we find that none do. This means that 997 is a prime number.
Therefore, the largest prime number less than 1000 is 997.
Keep in mind that this process can be time-consuming for larger numbers. There are more efficient algorithms for finding larger prime numbers. However, for numbers less than 1000, trial division is sufficient.