{"id":17525,"date":"2022-10-25T09:04:39","date_gmt":"2022-10-25T03:34:39","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-printing-prime-numbers-in-java\/"},"modified":"2022-10-25T09:04:39","modified_gmt":"2022-10-25T03:34:39","slug":"solved-printing-prime-numbers-in-java","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-printing-prime-numbers-in-java\/","title":{"rendered":"[Solved] printing Prime numbers in java"},"content":{"rendered":"

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The first loop just for generating numbers from 2 to 100.<\/p>\n

The second loop tries to find if the number is divisible by any other number. Here we try to divide a the number with a set of numbers (2 to prime_index). <\/p>\n

Let’s say the number is 10<\/code>, the prime index is 10\/2 = 5<\/code> for first iteration(j = 2). Which means, if the number 10<\/code> is not divisible by any number between 2 and 5, it’s a prime number. It’s divisible by 2<\/code> itself making it a non prime number.<\/p>\n

Let’s say the number is 9, now the prime index is 9\/2 = 4<\/code> for first iteration(j = 2). Now, 9 % 2<\/code> gives 1 as reminder. So, loop continues for second iteration (j = 3). Now the prime index is 9\/3 = 3<\/code> (Note here the prime index value is reduced from 4 to 3<\/strong>) So, now if the number is not divisible by 3<\/code>, its decided as a prime number.<\/p>\n

So, for every iteration, the prime index will reduce, making the number of iterations reduced.<\/p>\n

Example for Number 97,\nj = 2, prime index = 97\/2 = 48 (no of iterations for loop)\nj = 3, prime index = 97\/3 = 32 (no of iterations for loop)\nj = 4, prime index = 97\/4 = 24 (no of iterations for loop)\nj = 5, prime index = 97\/5 = 19 (no of iterations for loop)\nj = 6, prime index = 97\/6 = 16 (no of iterations for loop)\nj = 7, prime index = 97\/7 = 13 (no of iterations for loop)\nj = 8, prime index = 97\/8 = 12 (no of iterations for loop)\nj = 9, prime index = 97\/9 = 10 (no of iterations for loop)\nj = 10, prime index = 97\/10 = 9 (loop exits as condition failed 10 <= 9 and declares 97 as a prime number)\n<\/code><\/pre>\n
Now, here the loop actually took 10 iterations instead of the proposed 48 iterations.<\/p>\n
Let’s modify the code for better understanding.<\/p>\n
public static void main(String args[]) {    \n        \/\/ Number from 2 to 100\n    for(int i=2; i < 100; i++) { \n       if (isPrimeNumber(i)) {\n            System.out.println(i + \" is prime\");\n       }\n    }\n}\n<\/code><\/pre>\n
Now, lets see a method isPrimeNumberNotOptimized()<\/code> which is not optimized.<\/p>\n
private static boolean isPrimeNumberNotOptimized(int i) {\n    for(int j=2; j <= i\/2; j++) {\n        \/\/ if it is, then its not prime \n        if((i%j) == 0) {\n            return false;\n        }\n    }\n    return true; \n}\n<\/code><\/pre>\n
And, another method isPrimeNumberOptimized()<\/code> which is optimized with prime index.<\/p>\n
private static boolean isPrimeNumberOptimized(int i) {\n    for(int j=2; j <= i\/j; j++) {\n        \/\/ if it is, then its not prime \n        if((i%j) == 0) {\n            return false;\n        }\n    }\n    return true; \n}\n<\/code><\/pre>\n
Now, both methods will run and print the prime numbers correctly.<\/p>\n
But, the optimized method will decide 97<\/code> is a prime number at 10th iteration. <\/p>\n
And, the non-optimized method will decide the same in 48th iteration.<\/p>\n
Hope, you understand it now.<\/p>\n
FYI:<\/em><\/strong> prime index is the number we used for calculation. Such that if a number is not divisible between 2 & the derived prime index, its a prime number<\/p>\n<\/p><\/div>\n
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            1<\/span> <\/p><\/div>\n<\/div>\n
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solved printing Prime numbers in java <\/p>\n","protected":false},"excerpt":{"rendered":"
[ad_1] The first loop just for generating numbers from 2 to 100. The second loop tries to find if the number is divisible by any other number. Here we try to divide a the number with a set of numbers (2 to prime_index). Let’s say the number is 10, the prime index is 10\/2 = … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[320],"tags":[323],"class_list":["post-17525","post","type-post","status-publish","format-standard","hentry","category-solved","tag-java"],"yoast_head":"\n[Solved] printing Prime numbers in java - JassWeb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jassweb.com\/solved\/solved-printing-prime-numbers-in-java\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Solved] printing Prime numbers in java - JassWeb\" \/>\n<meta property=\"og:description\" content=\"[ad_1] The first loop just for generating numbers from 2 to 100. 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