Use the test for primality and the result of exercise to determine whether the following numbers are prime.
a. 9,269
b. 9,103
c. 8,623
d. 7,917
Exercise
The sieve of Eratosthenes, named after its inventor, the Greek scholar Eratosthenes (276-194 B.C.E.), provides a way to find all prime numbers less than or equal to some fixed number n. To construct it, write out all the integers from 2 to n. Cross out all multiples of 2 except 2 itself, then all multiples of 3 except 3 itself, then all multiples of 5 except 5 itself, and so forth. Continue crossing out the multiples of each successive prime number up to . The numbers that are not crossed out are all the prime numbers from 2 to n. Here is a sieve of Eratosthenes that includes the numbers from 2 to 27. The multiples of 2 are crossed out with a /, the multiples of 3 with a \, and the multiples of 5 with a —.
Use the sieve of Eratosthenes to find all prime numbers less than 100.
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