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 243112609 - 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?
M2 = 22 - 1 = 3
prime number
M3 = 23 - 1 = 7
prime number
M5 = 25 - 1 = 31
prime number
M7 = 27 - 1 = 127
prime number
M11 = 211 - 1 = 2047
= 23 * 89
M13 = 213 - 1 = 8191
prime number
M17 = 217 - 1 = 131071
prime number
M19 = 219 - 1 = 524287
prime number
M23 = 223 - 1 = 8388607
= 47 * 178481
M29 = 229 - 1 = 536870911
= 233 * 1103 * 2089
M31 = 231 - 1 = 2147483647
prime number
M37 = 237 - 1 = 137438953471
= 223 * 616318177
M41 = 241 - 1 = 2199023255551
= 13367 * 164511353
M43 = 243 - 1 = 8796093022207
= 431 * 9719 * 2099863
M47 = 247 - 1 = 140737488355327
= 2351 * 4513 * 13264529
M53 = 253 - 1 = 9007199254740991
= 6361 * 69431 * 20394401
M59 = 259 - 1 = 576460752303423487
= 179951 * 3203431780337
M61 = 261 - 1 = 2305843009213693951
prime number
M67 = 267 - 1 = 147573952589676412927
= 193707721 * 761838257287
M71 = 271 - 1 = 2361183241434822606847
= 228479 * 48544121 * 212885833
M73 = 273 - 1 = 9444732965739290427391
= 439 * 2298041 * 9361973132609
M79 = 279 - 1 = 604462909807314587353087
= 2687 * 202029703 * 1113491139767
M83 = 283 - 1 = 9671406556917033397649407
= 167 * 57912614113275649087721
M89 = 289 - 1 = 618970019642690137449562111
prime number
M97 = 297 - 1 = 158456325028528675187087900671
= 11447 * 13842607235828485645766393