for java programming A prime integer is any integer greater than 1 that can be d
ID: 3747720 • Letter: F
Question
for java programming
A prime integer is any integer greater than 1 that can be divided evenly only by itself and 1. The Sieve of Eratosthenes is a method of finding prime numbers. It works as follows: a) Create an array with all elements initialized to 1 (true). Array elements with prime subscripts will remain 1. All other array elements will eventually be set to zero. b) Starting with array subscript 2 (subscript 1 is not prime), every time an array element is found whose value is 1, loop through the remainder of the array and set to zero every element whose subscript is a multiple of the subscript for the element with value 1. For array subscript 2, all elements beyond 2 in the array that are multiples of 2 will be set to zero (subscripts 4, 6, 8, 10, and so on.). For array subscript 3, all elements beyond 3 in the array that are multiples of 3 will be set to zero (subscripts 6, 9, 12, 15, and so on.). When this process is complete, the array elements that are still set to 1 indicate that the subscript is a prime number. Write a program that uses an array of 1,000 elements to determine and print the prime numbers between 1 and 999. Ignore element 0 of the array.
Explanation / Answer
Program
public class SieveOfEratosthenes {
public static void main(String[] args)
{
System.out.println("Sieve Of Eratosthenes Prime Algorithm ");
int N=1000;
int[] arr = new int[N + 1];
for (int i = 2; i <= Math.sqrt(N); i++)
{
if (arr[i] == 0)
{
for (int j = i * i; j <= N; j += i)
{
arr[j] = 1;
}
}
}
System.out.println("The Prime numbers between 1 and 1000 are : ");
for (int i = 2; i < arr.length; i++)
if (arr[i] == 0)
System.out.println(i);
}
}
Output
run:
Sieve Of Eratosthenes Prime Algorithm
The Prime numbers between 1 and 1000 are :
2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97
101
103
107
109
113
127
131
137
139
149
151
157
163
167
173
179
181
191
193
197
199
211
223
227
229
233
239
241
251
257
263
269
271
277
281
283
293
307
311
313
317
331
337
347
349
353
359
367
373
379
383
389
397
401
409
419
421
431
433
439
443
449
457
461
463
467
479
487
491
499
503
509
521
523
541
547
557
563
569
571
577
587
593
599
601
607
613
617
619
631
641
643
647
653
659
661
673
677
683
691
701
709
719
727
733
739
743
751
757
761
769
773
787
797
809
811
821
823
827
829
839
853
857
859
863
877
881
883
887
907
911
919
929
937
941
947
953
967
971
977
983
991
997
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