メルセンヌ素数 (1～10000)

2^n - 1

2011現在 47 のメルセンヌ素数が知られている．最大のものは 2^43112609 - 1 で，これは 12,978,189 桁の数である．

未解決問題 : メルセンヌ素数は無限に存在するか？

メルセンヌ数 ( n : 素数 )

M₂	3	= 2² - 1	prime number
M₃	7	= 2³ - 1	prime number
M₅	31	= 2⁵ - 1	prime number
M₇	127	= 2⁷ - 1	prime number
M₁₁	2047	= 2¹¹ - 1	= 23 * 89
M₁₃	8191	= 2¹³ - 1	prime number
M₁₇	131071	= 2¹⁷ - 1	prime number
M₁₉	524287	= 2¹⁹ - 1	prime number
M₂₃	8388607	= 2²³ - 1	= 47 * 178481
M₂₉	536870911	= 2²⁹ - 1	= 233 * 1103 * 2089
M₃₁	2147483647	= 2³¹ - 1	prime number
M₃₇	137438953471	= 2³⁷ - 1	= 223 * 616318177
M₄₁	2199023255551	= 2⁴¹ - 1	= 13367 * 164511353
M₄₃	8796093022207	= 2⁴³ - 1	= 431 * 9719 * 2099863
M₄₇	140737488355327	= 2⁴⁷ - 1	= 2351 * 4513 * 13264529
M₅₃	9007199254740991	= 2⁵³ - 1	= 6361 * 69431 * 20394401
M₅₉	576460752303423487	= 2⁵⁹ - 1	= 179951 * 3203431780337
M₆₁	2305843009213693951	= 2⁶¹ - 1	prime number
M₆₇	147573952589676412927	= 2⁶⁷ - 1	= 193707721 * 761838257287
M₇₁	2361183241434822606847	= 2⁷¹ - 1	= 228479 * 48544121 * 212885833
M₇₃	9444732965739290427391	= 2⁷³ - 1	= 439 * 2298041 * 9361973132609
M₇₉	604462909807314587353087	= 2⁷⁹ - 1	= 2687 * 202029703 * 1113491139767
M₈₃	9671406556917033397649407	= 2⁸³ - 1	= 167 * 57912614113275649087721
M₈₉	618970019642690137449562111	= 2⁸⁹ - 1	prime number
M₉₇	158456325028528675187087900671	= 2⁹⁷ - 1	= 11447 * 13842607235828485645766393