Question 76
The sum of the cousins from 1 to 1000 is at most how much? Many years ago, a teacher who did not want to teach, ordered his students to calculate the sum of the numbers from 1 to 100.
$$
1+2+3+\ldots+n=\frac{n(n+1)}{2}
$$
As this story has been around for a long time, today the challenges given to students ask for more elaborate tasks.
a. Check that every prime number greater than 3 leaves 1 or 5 in the division by 6.
b. Check that the sum of the prime numbers that are greater than 1 and less than 1000 is less than 166338.
c. In the above estimate, to have fewer technical complications, we did not eliminate some numbers that are certainly not prime. Eliminate some of these numbers and check that the sum of the primes that are greater than 1 and less than 1000 is less than 166000.
$$
1+2+3+\ldots+n=\frac{n(n+1)}{2}
$$
As this story has been around for a long time, today the challenges given to students ask for more elaborate tasks.
a. Check that every prime number greater than 3 leaves 1 or 5 in the division by 6.
b. Check that the sum of the prime numbers that are greater than 1 and less than 1000 is less than 166338.
c. In the above estimate, to have fewer technical complications, we did not eliminate some numbers that are certainly not prime. Eliminate some of these numbers and check that the sum of the primes that are greater than 1 and less than 1000 is less than 166000.