Individual Exercise: Sieve of Eratosthenes O The Sieve of Eratosthenes is a technique for finding all the prime numbers up to a given last number. o It can be implemented as a program by using the algorithm (steps) given below. " Create a variable for the last number initialized as 100 etc. (e.g., int lastNumber = 100;) • Create a boolean array isPrime[] to keep track of which numbers up to lastNumber are prime. O The length of the array must be equal to lastNumber + 1 as the array indexes start from zero. O Note: The default value is false for all the array elements when a boolean array is created by using new. • Set all the array elements beginning from index = 2 (the first prime number) to true. ' Outer loop: Repeat the following steps for each number num within 2 <= num <= lastNumber / num. o if isPrime[num] is true (meaning that num is prime as no factors exist for num): * Inner loop: Set the isPrime[] elements for all the multiples of num to false. O When the nested loop ends, isPrime[num] is true if and only if num is a prime number. O Print all the prime numbers up to lastNumber as the numbers (num) for which the corresponding element in the isPrime array (i.e., isPrime[num]) is true. Expected Console Output of the Program for lastNumber = 100: All the prime numbers up to 100 are 2357 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
Individual Exercise: Sieve of Eratosthenes O The Sieve of Eratosthenes is a technique for finding all the prime numbers up to a given last number. o It can be implemented as a program by using the algorithm (steps) given below. " Create a variable for the last number initialized as 100 etc. (e.g., int lastNumber = 100;) • Create a boolean array isPrime[] to keep track of which numbers up to lastNumber are prime. O The length of the array must be equal to lastNumber + 1 as the array indexes start from zero. O Note: The default value is false for all the array elements when a boolean array is created by using new. • Set all the array elements beginning from index = 2 (the first prime number) to true. ' Outer loop: Repeat the following steps for each number num within 2 <= num <= lastNumber / num. o if isPrime[num] is true (meaning that num is prime as no factors exist for num): * Inner loop: Set the isPrime[] elements for all the multiples of num to false. O When the nested loop ends, isPrime[num] is true if and only if num is a prime number. O Print all the prime numbers up to lastNumber as the numbers (num) for which the corresponding element in the isPrime array (i.e., isPrime[num]) is true. Expected Console Output of the Program for lastNumber = 100: All the prime numbers up to 100 are 2357 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
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![Individual Exercise: Sieve of Eratosthenes
O The Sieve of Eratosthenes is a technique for finding all the prime numbers up to a given last number.
o It can be implemented as a program by using the algorithm (steps) given below.
" Create a variable for the last number initialized as 100 etc. (e.g., int lastNumber = 100;)
• Create a boolean array isPrime[] to keep track of which numbers up to lastNumber are prime.
O The length of the array must be equal to lastNumber + 1 as the array indexes start from zero.
o Note: The default value is false for all the array elements when a boolean array is created by using new.
' Set all the array elements beginning from index = 2 (the first prime number) to true.
' Outer loop: Repeat the following steps for each number num within 2 <= num <= lastNumber / num.
o if isPrime[num] is true (meaning that num is prime as no factors exist for num):
" Inner loop: Set the isPrime[] elements for all the multiples of num to false.
O When the nested loop ends, isPrime[num] is true if and only if num is a prime number.
O Print all the prime numbers up to lastNumber as the numbers (num) for which the corresponding element in
the isPrime array (i.e., isPrime[num]) is true.
Expected Console Output of the Program for lastNumber = 100:
All the prime numbers up to 100 are
2357 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56948d1f-f3cf-4f40-ab0a-6067bba5bbc4%2F093c57e5-da21-4763-ab51-425dcf8ef9e3%2Ft3i4mw8_processed.png&w=3840&q=75)
Transcribed Image Text:Individual Exercise: Sieve of Eratosthenes
O The Sieve of Eratosthenes is a technique for finding all the prime numbers up to a given last number.
o It can be implemented as a program by using the algorithm (steps) given below.
" Create a variable for the last number initialized as 100 etc. (e.g., int lastNumber = 100;)
• Create a boolean array isPrime[] to keep track of which numbers up to lastNumber are prime.
O The length of the array must be equal to lastNumber + 1 as the array indexes start from zero.
o Note: The default value is false for all the array elements when a boolean array is created by using new.
' Set all the array elements beginning from index = 2 (the first prime number) to true.
' Outer loop: Repeat the following steps for each number num within 2 <= num <= lastNumber / num.
o if isPrime[num] is true (meaning that num is prime as no factors exist for num):
" Inner loop: Set the isPrime[] elements for all the multiples of num to false.
O When the nested loop ends, isPrime[num] is true if and only if num is a prime number.
O Print all the prime numbers up to lastNumber as the numbers (num) for which the corresponding element in
the isPrime array (i.e., isPrime[num]) is true.
Expected Console Output of the Program for lastNumber = 100:
All the prime numbers up to 100 are
2357 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
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