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4. Prime Numbers in Range

{
  "topic": "primes-in-range",
  "input_types": [
    "int",
    "int"
  ],
  "input_labels": [
    "m",
    "n"
  ],
  "input_values": [
    "13",
    "100"
  ],
  "type": "Calculate",
  "title": "Prime Numbers in Range",
  "category": "Arithmetic",
  "function": "function myFunc(arr) {\n        let m = arr[0];\n        let n = arr[1];\n        if (m > n || m < 2) {\n          return \"Invalid range. Please make sure m <= n, m > 2.\";\n        }\n      \n        const isPrime = (number) => {\n          if (number < 2) {\n            return false;\n          }\n      \n          for (let i = 2; i <= Math.sqrt(number); i++) {\n            if (number % i === 0) {\n              return false;\n            }\n          }\n      \n          return true;\n        };\n      \n        const primes = [];\n      \n        for (let i = m; i <= n; i++) {\n          if (isPrime(i)) {\n            primes.push(i);\n          }\n        }\n      \n        return primes.join(\", \");\n      }",
  "op_label": "Prime Numbers in [m,n]",
  "explanation": "An integer is a Prime number if it has only two factors: one and itself.",
  "content": "<h2>Finding Prime Numbers in a Given Range</h2>\n<p>A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. When given a range, we can find all prime numbers within that range by checking each number individually to see if it is prime.</p>\n<p>The process involves checking divisibility for each number starting from the lower bound up to the upper bound of the range. A number is prime if it has no divisors other than 1 and itself, meaning it cannot be evenly divided by any number other than 1 and itself.</p>\n\n<h2>Examples</h2>\n<p>Let’s explore some examples to see how we can find prime numbers within a specific range.</p>\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">1.</span> Find all prime numbers between 13 and 100.</h3><h4 class=\"answer\">Answer</h4>\n<p>First, we identify the given range:</p>\n<p><b>Given:</b></p><ul><li><b>m</b> = 13</li><li><b>n</b> = 100</li></ul>\n<p>We then check each number from 13 to 100 to determine if it is prime. The prime numbers in this range are found by checking divisibility for each number:</p>\n<p><b>Prime Numbers:</b></p><ul><li>13: Prime</li>\n<li>17: Prime</li>\n<li>19: Prime</li>\n<li>23: Prime</li>\n<li>29: Prime</li>\n<li>31: Prime</li>\n<li>37: Prime</li>\n<li>41: Prime</li>\n<li>43: Prime</li>\n<li>47: Prime</li>\n<li>53: Prime</li>\n<li>59: Prime</li>\n<li>61: Prime</li>\n<li>67: Prime</li>\n<li>71: Prime</li>\n<li>73: Prime</li>\n<li>79: Prime</li>\n<li>83: Prime</li>\n<li>89: Prime</li>\n<li>97: Prime</li></ul>\n<p>These numbers have no divisors other than 1 and themselves, so they are prime.</p>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The prime numbers between 13 and 100 are: 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">2.</span> Find prime numbers between 50 and 75.</h3><h4 class=\"answer\">Answer</h4>\n<p>We begin by identifying the range:</p>\n<p><b>Given:</b></p><ul><li><b>m</b> = 50</li><li><b>n</b> = 75</li></ul>\n<p>Next, we check each number from 50 to 75 to see if it is prime:</p>\n<p><b>Prime Numbers:</b></p><ul><li>53: Prime</li>\n<li>59: Prime</li>\n<li>61: Prime</li>\n<li>67: Prime</li>\n<li>71: Prime</li>\n<li>73: Prime</li></ul>\n<p>These numbers are not divisible by any number other than 1 and themselves.</p>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The prime numbers between 50 and 75 are: 53, 59, 61, 67, 71, 73.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">3.</span> Determine the prime numbers from 20 to 50.</h3><h4 class=\"answer\">Answer</h4>\n<p>First, we identify the range:</p>\n<p><b>Given:</b></p><ul><li><b>m</b> = 20</li><li><b>n</b> = 50</li></ul>\n<p>We then check each number from 20 to 50 to find the prime numbers:</p>\n<p><b>Prime Numbers:</b></p><ul><li>23: Prime</li>\n<li>29: Prime</li>\n<li>31: Prime</li>\n<li>37: Prime</li>\n<li>41: Prime</li>\n<li>43: Prime</li>\n<li>47: Prime</li></ul>\n<p>These numbers are identified as prime because they have no divisors other than 1 and themselves.</p>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The prime numbers between 20 and 50 are: 23, 29, 31, 37, 41, 43, 47.</p></div>\n\n<div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">4.</span> Find the prime numbers between 90 and 120.</h3><h4 class=\"answer\">Answer</h4>\n<p>We begin by identifying the range:</p>\n<p><b>Given:</b></p><ul><li><b>m</b> = 90</li><li><b>n</b> = 120</li></ul>\n<p>We then check each number from 90 to 120 to determine if it is prime:</p>\n<p><b>Prime Numbers:</b></p><ul><li>97: Prime</li>\n<li>101: Prime</li>\n<li>103: Prime</li>\n<li>107: Prime</li>\n<li>109: Prime</li>\n<li>113: Prime</li></ul>\n<p>These numbers are prime because they are only divisible by 1 and themselves.</p>\n<p><b>Result:</b></p><p class=\"tabspace answer\">∴ The prime numbers between 90 and 120 are: 97, 101, 103, 107, 109, 113.</p></div>"
}