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非法質數

非法質數（英語：Illegal prime），是指同時也是質數的非法数字。在2001年3月，菲尔·卡莫迪（Phil Carmody）創造了最早的非法質數。由於這類數字的二進位表示法包含了以C語言編寫、經壓縮處理後的DeCSS解密算法原始碼，因此计算机可以使用它来繞過DVD的复制保护措施。^[1]

參考資料

^ Prime glossary - Illegal prime. Primes.utm.edu. 1999-10-06 [2013-03-26]. （原始内容存档于2021-05-09）.

相關條目

查论编質數類

公式	卡羅爾（ $（2 n －1） 2 －2$ ）費馬質數（ $2 2 n ＋1$ ）梅森質數（ $2 p －1$ ）雙重梅森質數（ $2 2 p －1 －1$ ）瓦格斯塔夫質數 $（2 p ＋1）／3$ 普羅斯質數（ $k \cdot2 n ＋1$ ）階乘質數（ $n ！\pm1$ ）質數階乘質數（ $p n ＃\pm1$ ）歐幾里得數（ $p n ＃＋1$ ）畢達哥拉斯質數（ $4 n ＋1$ ）皮爾龐特質數（ $2 m \cdot3 n ＋1$ ） Quartan質數（ $x 4 ＋ y 4$ ）（英语：Quartan prime）索利納斯質數（ $2 m \pm2 n \pm1$ ）（英语：Solinas prime）卡倫質數（ $n \cdot2 n ＋1$ ）胡道爾質數（ $n \cdot2 n －1$ ）立方質數（ $x 3 － y 3 ）／（ x － y$ ）萊蘭質數（ $x y ＋ y x$ ）塔別脫質數（ $3\cdot2 n －1$ ）威廉姆斯素数（ $（ b -1）\cdot b n －1$ ）（英语：Williams number）米爾斯質數（［ $A 3 n$ ］） Kynea質數（ $（2 n ＋1） 2 －2$ ）

整數數列	斐波纳契素数盧卡斯質數佩尔質數 NSW質數佩蘭偽質數

屬性	維費里希質數質數對（英语：Wieferich pair）沃尔-孙-孙質數沃爾斯滕霍爾姆質數（英语：Wolstenholme prime）威尔逊素数幸运質數 Fortunate質數（英语：Fortunate number）拉馬努金質數皮萊質數正則質數强質數斯特恩質數超奇異質數（橢圓曲線）（英语：Supersingular prime (algebraic number theory)）超奇異質數（月光理論）好質數超質數希格斯質數高互補歐拉商數唯一質數

基數相關	回文素数反素数循環單位質數 $（10 n －1）／9$ 可交换質數環狀質數可截短質數極小質數精緻質數（英语：Delicate prime）原始質數全循環質數唯一質數快樂質數自我質數 Smarandache–Wellin質數 Strobogrammatic質數（英语：Strobogrammatic prime）二面質數四面質數（英语：Tetradic number）

圖形	孪生質數（ $p ， p ＋2$ ）孪生倍链（ $n \pm 1，2 n \pm 1，4 n \pm 1，\dots$ ）（英语：Bi-twin chain）三胞胎質數（ $p ， p ＋2 或 p ＋4， p ＋6$ ）四胞胎質數（ $p ， p ＋2， p ＋6， p ＋8$ ）質數k元組（英语：Prime k-tuple）表兄弟質數（ $p ， p ＋4$ ）六質數（ $p ， p ＋6$ ）陈質數索菲·熱爾曼／安全質數（ $p ，2 p ＋1$ ）坎寧安鏈（ $p ，2 p \pm 1，4 p \pm 3，8 p \pm 7，...$ ）（英语：Cunningham chain）等差數列（ $p ＋ a\cdotn ， n ＝0，1，2，3，...$ ）（英语：Primes in arithmetic progression）平衡質數（ $連續的 p － n ， p ， p ＋ n$ ）

數量級	超大質數（1,000,000+以上）（英语：Megaprime）已知最大質數列表（英语：List of largest known primes and probable primes）

复数	艾森斯坦質數高斯質數

合数	伪質數卡塔蘭（英语：Catalan pseudoprime）橢圓（英语：Elliptic pseudoprime）欧拉欧拉-雅可比费马弗羅貝尼烏斯（英语：Frobenius pseudoprime）盧卡斯（英语：Lucas pseudoprime）佩蘭索默爾–盧卡斯（英语：Somer–Lucas pseudoprime）強卡邁克爾數殆質數半質數楔形数 Interprime 有害数（英语：Pernicious number）

相關	準質數（英语：Probable prime）產業等級質數非法質數質數公式質數間隙 $X 2 ＋1$ 質數質數定理素数计数函数素性测试

前60個質數	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

質數列表

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非法質數

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