{"id":1801,"date":"2026-01-12T15:06:42","date_gmt":"2026-01-12T12:06:42","guid":{"rendered":"https:\/\/markahost.com.tr\/blog\/?p=1801"},"modified":"2026-01-12T15:06:42","modified_gmt":"2026-01-12T12:06:42","slug":"python-asal-sayi-bulma","status":"publish","type":"post","link":"https:\/\/markahost.com.tr\/blog\/python-asal-sayi-bulma\/","title":{"rendered":"Python Asal Say\u0131 Bulma: Algoritmalar, \u00d6rnekler ve Uygulamalar"},"content":{"rendered":"

Python\u00a0Asal Say\u0131 Bulma<\/strong>: Algoritmalar, \u00d6rnekler ve Uygulamalar<\/h2>\n

Asal say\u0131lar, matematiksel bir kavramd\u0131r ve sadece kendileri ve 1’e b\u00f6l\u00fcnebilen say\u0131lard\u0131r. Asall\u0131k testi, bir say\u0131n\u0131n asal olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r.\u00a0Python, Asal Say\u0131lar\u0131 bulma<\/strong>k i\u00e7in bir\u00e7ok algoritma<\/a> ve y\u00f6ntem sunar. Bu yaz\u0131da,\u00a0Python’da Asal Say\u0131lar\u0131 bulma<\/strong>n\u0131n farkl\u0131 y\u00f6ntemlerini ve \u00f6rneklerini inceleyece\u011fiz.<\/p>\n

Asal Say\u0131 Nedir?<\/strong><\/h2>\n

Asal say\u0131lar, sadece kendileri ve 1’e b\u00f6l\u00fcnebilen say\u0131lard\u0131r. \u00d6rne\u011fin, 2, 3, 5, 7, 11, 13, 17, 19, 23 gibi say\u0131lar\u00a0Asal Say\u0131<\/strong>lard\u0131r. Ancak, 4, 6, 8, 9, 10, 12 gibi say\u0131lar\u00a0Asal Say\u0131<\/strong>\u00a0de\u011fildir.<\/p>\n

Asal Say\u0131<\/strong>lar\u0131n \u00d6zellikleri<\/h2>\n

Asal say\u0131lar\u0131n bir\u00e7ok \u00f6zelli\u011fi vard\u0131r. \u0130\u015fte baz\u0131lar\u0131:<\/p>\n

    \n
  • Asal say\u0131lar sadece kendileriyle ve 1 ile b\u00f6l\u00fcnebilirler.<\/li>\n
  • Her do\u011fal say\u0131,\u00a0Asal Say\u0131<\/strong>lar\u0131n \u00e7arp\u0131m\u0131 \u015feklinde yaz\u0131labilir.<\/li>\n
  • En k\u00fc\u00e7\u00fck\u00a0Asal Say\u0131<\/strong>\u00a02’dir.<\/li>\n
  • Asal say\u0131lar\u0131n sonsuz say\u0131da oldu\u011fu kan\u0131tlanm\u0131\u015ft\u0131r.<\/li>\n<\/ul>\n

    Asal Say\u0131lar\u0131 Bulman\u0131n Y\u00f6ntemleri<\/h2>\n

    Asal say\u0131lar\u0131 bulmak i\u00e7in bir\u00e7ok y\u00f6ntem vard\u0131r. \u0130\u015fte baz\u0131lar\u0131:<\/p>\n

    1. Kuvvet Metodu<\/h3>\n

    Kuvvet metodu, bir say\u0131n\u0131n asal olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131lan basit bir y\u00f6ntemdir. Bu y\u00f6ntemde, bir say\u0131n\u0131n 2’den kendisine kadar olan t\u00fcm say\u0131larla b\u00f6l\u00fcn\u00fcp b\u00f6l\u00fcnemedi\u011fi kontrol edilir. E\u011fer hi\u00e7bir say\u0131ya b\u00f6l\u00fcnemiyorsa, say\u0131 asal olarak kabul edilir.<\/p>\n

    2. Deneme B\u00f6lme Y\u00f6ntemi<\/h3>\n

    Deneme b\u00f6lme y\u00f6ntemi, bir say\u0131n\u0131n asal olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131lan bir ba\u015fka basit y\u00f6ntemdir. Bu y\u00f6ntemde, bir say\u0131n\u0131n 2’den kendisine kadar olan t\u00fcm say\u0131larla b\u00f6l\u00fcn\u00fcp b\u00f6l\u00fcnemedi\u011fi kontrol edilir. Ancak, bu y\u00f6ntem kaba bir y\u00f6ntemdir ve b\u00fcy\u00fck say\u0131lar i\u00e7in \u00e7ok zaman al\u0131r.<\/p>\n

    3. Fermat Testi<\/h3>\n

    Fermat testi, bir say\u0131n\u0131n asal olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131lan bir di\u011fer y\u00f6ntemdir. Bu y\u00f6ntemde, bir say\u0131n\u0131n asal olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in Fermat teoremi kullan\u0131l\u0131r. Fermat teoremi, p ve a tam say\u0131lar\u0131 olmak \u00fczere, a^(p-1) \u2261 1 (mod p) e\u015fitli\u011fi \u015feklinde ifade edilir. E\u011fer bu e\u015fitlik sa\u011flan\u0131yorsa, say\u0131 asal olarak kabul edilir.<\/p>\n

    4. Miller-Rabin Testi<\/h3>\n

    Miller-Rabin testi, bir say\u0131n\u0131n asal olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131lan bir di\u011fer y\u00f6ntemdir. Bu y\u00f6ntemde, bir say\u0131n\u0131n asal olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in Rabin-Miller teoremi kullan\u0131l\u0131r. Rabin-Miller teoremi, bir say\u0131n\u0131n asal olma olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131l\u0131r.<\/p>\n

    5. Eratosthenes Y\u00f6ntemi<\/h3>\n

    Eratosthenes y\u00f6ntemi, belirli bir aral\u0131ktaki t\u00fcm\u00a0Asal Say\u0131<\/strong>lar\u0131 bulmak i\u00e7in kullan\u0131lan bir y\u00f6ntemdir. Bu y\u00f6ntemde, bir say\u0131n\u0131n asal olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in 2’den ba\u015flayarak t\u00fcm say\u0131lar kontrol edilir. E\u011fer bir say\u0131 asal olarak kabul edilirse, bu say\u0131n\u0131n katlar\u0131 \u00e7\u0131kar\u0131l\u0131r ve kalan say\u0131lar tekrar kontrol edilir.<\/p>\n

    6. Atkins Y\u00f6ntemi<\/h3>\n

    Atkins y\u00f6ntemi, belirli bir aral\u0131ktaki t\u00fcm\u00a0Asal Say\u0131<\/strong>lar\u0131 bulmak i\u00e7in kullan\u0131lan bir y\u00f6ntemdir. Bu y\u00f6ntem, Eratosthenes y\u00f6ntemine benzer \u015fekilde \u00e7al\u0131\u015f\u0131r, ancak daha h\u0131zl\u0131d\u0131r. Atkins y\u00f6ntemi, 2, 3 ve 5 say\u0131lar\u0131n\u0131 baz al\u0131r ve bu say\u0131lar\u0131n katlar\u0131ndan olu\u015fan bir liste olu\u015fturur. Daha sonra, bu listedeki say\u0131lar \u00fczerinde \u00e7e\u015fitli i\u015flemler yaparak\u00a0Asal Say\u0131<\/strong>lar\u0131 bulur.<\/p>\n

    Python’da\u00a0Asal Say\u0131<\/strong>lar\u0131 Bulma<\/h2>\n

    Python,\u00a0Asal Say\u0131<\/strong>lar\u0131 bulmak i\u00e7in bir\u00e7ok algoritma ve y\u00f6ntem sunar. \u0130\u015fte baz\u0131lar\u0131:<\/p>\n

    1. Kuvvet Metodu ile\u00a0Asal Say\u0131 Bulma<\/strong><\/h3>\n
    \n
    <\/div>\n
    def<\/span> is_prime<\/span>(n<\/span>):\r\n    if<\/span> n <= 1<\/span>:\r\n        return<\/span> False<\/span>\r\n    for<\/span> i in<\/span> range<\/span>(2<\/span>, n):\r\n        if<\/span> n % i == 0<\/span>:\r\n            return<\/span> False<\/span>\r\n    return<\/span> True<\/span>\r\n<\/code><\/pre>\n<\/div>\n
    Bu kod, kuvvet metodu ile bir say\u0131n\u0131n asal olup olmad\u0131\u011f\u0131n\u0131 kontrol eder. E\u011fer say\u0131 asal ise True, de\u011filse False d\u00f6nd\u00fcr\u00fcr.<\/p>\n
    2. Deneme B\u00f6lme Y\u00f6ntemi ile\u00a0Asal Say\u0131 Bulma<\/strong><\/h3>\n
    \n
    <\/div>\n
    def<\/span> is_prime<\/span>(n<\/span>):\r\n    if<\/span> n <= 1<\/span>:\r\n        return<\/span> False<\/span>\r\n    elif<\/span> n <= 3<\/span>:\r\n        return<\/span> True<\/span>\r\n    elif<\/span> n % 2<\/span> == 0<\/span> or<\/span> n % 3<\/span> == 0<\/span>:\r\n        return<\/span> False<\/span>\r\n    i = 5<\/span>\r\n    while<\/span> i * i <= n:\r\n        if<\/span> n % i == 0<\/span> or<\/span> n % (i + 2<\/span>) == 0<\/span>:\r\n            return<\/span> False<\/span>\r\n        i += 6<\/span>\r\n    return<\/span> True<\/span>\r\n<\/code><\/pre>\n<\/div>\n
    Bu kod, deneme b\u00f6lme y\u00f6ntemi ile bir say\u0131n\u0131n asal olup olmad\u0131\u011f\u0131n\u0131 kontrol eder. Bu y\u00f6ntem, kuvvet metodu ile kar\u015f\u0131la\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda daha h\u0131zl\u0131d\u0131r.<\/p>\n
    3. Fermat Testi ile\u00a0Asal Say\u0131 Bulma<\/strong><\/h3>\n
    \n
    <\/div>\n
    import<\/span> random\r\n\r\ndef<\/span> is_prime<\/span>(n, k=5<\/span><\/span>):\r\n    if<\/span> n <= 1<\/span>:\r\n        return<\/span> False<\/span>\r\n    elif<\/span> n <= 3<\/span>:\r\n        return<\/span> True<\/span>\r\n    elif<\/span> n % 2<\/span> == 0<\/span> or<\/span> n % 3<\/span> == 0<\/span>:\r\n        return<\/span> False<\/span>\r\n    for<\/span> i in<\/span> range<\/span>(k):\r\n        a = random.randint(2<\/span>, n - 2<\/span>)\r\n        if<\/span> pow<\/span>(a, n - 1<\/span>, n) != 1<\/span>:\r\n            return<\/span> False<\/span>\r\n    return<\/span> True<\/span>\r\n<\/code><\/pre>\n<\/div>\n
    Bu kod, Fermat testi ile bir say\u0131n\u0131n asal olup olmad\u0131\u011f\u0131n\u0131 kontrol eder. Bu y\u00f6ntem, deneme b\u00f6lme y\u00f6ntemi ile kar\u015f\u0131la\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda daha h\u0131zl\u0131d\u0131r.<\/p>\n
    4. Miller-Rabin Testi ile\u00a0Asal Say\u0131 Bulma<\/strong><\/h3>\n
    \n
    <\/div>\n
    import<\/span> random\r\n\r\ndef<\/span> is_prime<\/span>(n, k=5<\/span><\/span>):\r\n    if<\/span> n <= 1<\/span>:\r\n        return<\/span> False<\/span>\r\n    elif<\/span> n <= 3<\/span>:\r\n        return<\/span> True<\/span>\r\n    elif<\/span> n % 2<\/span> == 0<\/span> or<\/span> n % 3<\/span> == 0<\/span>:\r\n        return<\/span> False<\/span>\r\n    r, s = 0<\/span>, n - 1<\/span>\r\n    while<\/span> s % 2<\/span> == 0<\/span>:\r\n        r += 1<\/span>\r\n        s \/\/= 2<\/span>\r\n    for<\/span> i in<\/span> range<\/span>(k):\r\n        a = random.randint(2<\/span>, n - 2<\/span>)\r\n        x = pow<\/span>(a, s, n)\r\n        if<\/span> x == 1<\/span> or<\/span> x == n - 1<\/span>:\r\n            continue<\/span>\r\n        for<\/span> j in<\/span> range<\/span>(r - 1<\/span>):\r\n            x = pow<\/span>(x, 2<\/span>, n)\r\n            if<\/span> x == n - 1<\/span>:\r\n                break<\/span>\r\n        else<\/span>:\r\n            return<\/span> False<\/span>\r\n    return<\/span> True<\/span>\r\n<\/code><\/pre>\n<\/div>\n
    Bu kod, Miller-Rabin testi ile bir say\u0131n\u0131n asal olup olmad\u0131\u011f\u0131n\u0131 kontrol eder. Bu y\u00f6ntem, Fermat testi ile kar\u015f\u0131la\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda daha g\u00fcvenilirdir.<\/p>\n
    5. Eratosthenes Y\u00f6ntemi ile\u00a0Asal Say\u0131 Bulma<\/strong><\/h3>\n
    \n
    <\/div>\n
    def<\/span> sieve<\/span>(n<\/span>):\r\n    primes = [True<\/span>] * (n + 1<\/span>)\r\n    primes[0<\/span>] = primes[1<\/span>] = False<\/span>\r\n    for<\/span> i in<\/span> range<\/span>(2<\/span>, int<\/span>(n ** 0.5<\/span>) + 1<\/span>):\r\n        if<\/span> primes[i]:\r\n            for<\/span> j in<\/span> range<\/span>(i * i, n + 1<\/span>, i):\r\n                primes[j] = False<\/span>\r\n    return<\/span> [i for<\/span> i in<\/span> range<\/span>(n + 1<\/span>) if<\/span> primes[i]]\r\n<\/code><\/pre>\n<\/div>\n
    Bu kod, Eratosthenes y\u00f6ntemi ile belirli bir aral\u0131ktaki t\u00fcm\u00a0Asal Say\u0131<\/strong>lar\u0131 bulur.<\/p>\n
    6. Atkins Y\u00f6ntemi ile\u00a0Asal Say\u0131 Bulma<\/strong><\/h3>\n
    \n
    <\/div>\n
    def<\/span> atkins<\/span>(n<\/span>):\r\n    primes = [False<\/span>] * (n + 1<\/span>)\r\n    sqrt_n = int<\/span>(n ** 0.5<\/span>) + 1<\/span>\r\n    for<\/span> x in<\/span> range<\/span>(1<\/span>, sqrt_n):\r\n        for<\/span> y in<\/span> range<\/span>(1<\/span>, sqrt_n):\r\n            z = 4<\/span> * x ** 2<\/span> + y ** 2<\/span>\r\n            if<\/span> z <= n and<\/span> (z % 12<\/span> == 1<\/span> or<\/span> z % 12<\/span> == 5<\/span>):\r\n                primes[z] = not<\/span> primes[z]\r\n            z = 3<\/span> * x ** 2<\/span> + y ** 2<\/span>\r\n            if<\/span> z <= n and<\/span> z % 12<\/span> == 7<\/span>:\r\n                primes[z] = not<\/span> primes[z]\r\n            z = 3<\/span> * x ** 2<\/span> - y ** 2<\/span>\r\n            if<\/span> x > y and<\/span> z <= n and<\/span> z % 12<\/span> == 11<\/span>:\r\n                primes[z] = not<\/span> primes[z]\r\n    for<\/span> i in<\/span> range<\/span>(5<\/span>, sqrt_n):\r\n        if<\/span> primes[i]:\r\n            for<\/span> j in<\/span> range<\/span>(i ** 2<\/span>, n + 1<\/span>, i ** 2<\/span>):\r\n                primes[j] = False<\/span>\r\n    return<\/span> [2<\/span>, 3<\/span>] + [i for<\/span> i in<\/span> range<\/span>(5<\/span>, n + 1<\/span>) if<\/span> primes[i]]\r\n<\/code><\/pre>\n<\/div>\n
    Bu kod, Atkins y\u00f6ntemi ile belirli bir aral\u0131ktaki t\u00fcm\u00a0Asal Say\u0131<\/strong>lar\u0131 bulur.<\/p>\n
    \u00d6rnekler<\/strong><\/h2>\n
      \n
    1. 37 say\u0131s\u0131\u00a0Asal Say\u0131<\/strong>d\u0131r.<\/li>\n
    2. 100 say\u0131s\u0131\u00a0Asal Say\u0131<\/strong>\u00a0de\u011fildir.<\/li>\n
    3. 457 say\u0131s\u0131\u00a0Asal Say\u0131<\/strong>d\u0131r.<\/li>\n
    4. 1000 say\u0131s\u0131\u00a0Asal Say\u0131<\/strong>\u00a0de\u011fildir.<\/li>\n<\/ol>\n
      Uygulamalar<\/strong><\/h2>\n
      Asal say\u0131lar, kriptografi, matematik, bilgisayar bilimi ve di\u011fer bir\u00e7ok alanda kullan\u0131l\u0131r. \u00d6rne\u011fin:<\/p>\n
        \n
      • Kriptografi:\u00a0Asal Say\u0131<\/strong>lar, \u015fifreleme algoritmalar\u0131nda kullan\u0131l\u0131r.<\/li>\n
      • Matematik:\u00a0Asal Say\u0131<\/strong>lar, matemati\u011fin bir\u00e7ok alan\u0131nda kullan\u0131l\u0131r.<\/li>\n
      • Bilgisayar Bilimi:\u00a0Asal Say\u0131<\/strong>lar, veri \u015fifreleme, rastgele say\u0131 olu\u015fturma ve di\u011fer bir\u00e7ok alanda kullan\u0131l\u0131r.<\/li>\n<\/ul>\n
        Sonu\u00e7<\/h2>\n
        Python, Asal Say\u0131lar\u0131 bulma<\/strong>k i\u00e7in bir\u00e7ok algoritma ve y\u00f6ntem sunar. Bu yaz\u0131da, kuvvet metodu, deneme b\u00f6lme y\u00f6ntemi, Fermat testi, Miller-Rabin testi, Eratosthenes y\u00f6ntemi ve Atkins y\u00f6ntemi gibi y\u00f6ntemlerin Python’da nas\u0131l uygulanaca\u011f\u0131n\u0131 inceledik. Ayr\u0131ca,\u00a0Asal Say\u0131<\/strong>lar\u0131n \u00f6zellikleri, \u00f6rnekleri ve uygulamalar\u0131 hakk\u0131nda bilgi verdik.<\/p>\n","protected":false},"excerpt":{"rendered":"
        Python\u00a0Asal Say\u0131 Bulma: Algoritmalar, \u00d6rnekler ve Uygulamalar Asal say\u0131lar, matematiksel bir kavramd\u0131r ve sadece kendileri ve 1’e b\u00f6l\u00fcnebilen say\u0131lard\u0131r. Asall\u0131k<\/p>\n","protected":false},"author":2,"featured_media":1802,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"rank_math_lock_modified_date":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1801","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-genel"],"_links":{"self":[{"href":"https:\/\/markahost.com.tr\/blog\/wp-json\/wp\/v2\/posts\/1801","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/markahost.com.tr\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/markahost.com.tr\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/markahost.com.tr\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/markahost.com.tr\/blog\/wp-json\/wp\/v2\/comments?post=1801"}],"version-history":[{"count":1,"href":"https:\/\/markahost.com.tr\/blog\/wp-json\/wp\/v2\/posts\/1801\/revisions"}],"predecessor-version":[{"id":1803,"href":"https:\/\/markahost.com.tr\/blog\/wp-json\/wp\/v2\/posts\/1801\/revisions\/1803"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/markahost.com.tr\/blog\/wp-json\/wp\/v2\/media\/1802"}],"wp:attachment":[{"href":"https:\/\/markahost.com.tr\/blog\/wp-json\/wp\/v2\/media?parent=1801"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/markahost.com.tr\/blog\/wp-json\/wp\/v2\/categories?post=1801"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/markahost.com.tr\/blog\/wp-json\/wp\/v2\/tags?post=1801"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}