Primes just less than a power of two
8 to 100 bits (page 1 of 4)
Here is a frequently asked question at the Prime Pages:
I am working on an algorithm and need a few of the largest primes with 64 bits. Where can I find them?To which we answer "here!" Below, for each consecutive value of n we give the ten least positive integers k such that 2n-k is a prime. In each case these are proven primes (proven using UBASIC's APRT-CL). Note that 2n-k will be an n bit number (for these k's).
n | ten least k's for which 2n-k is prime. |
---|---|
8 | 5, 15, 17, 23, 27, 29, 33, 45, 57, 59 |
9 | 3, 9 13, 21, 25, 33, 45, 49, 51, 55 |
10 | 3, 5 11, 15, 27, 33, 41, 47, 53, 57 |
11 | 9, 19, 21, 31, 37, 45, 49, 51, 55, 61 |
12 | 3, 5 17, 23, 39, 45, 47, 69, 75, 77 |
13 | 1, 13, 21, 25, 31, 45, 69, 75, 81, 91 |
14 | 3, 15, 21, 23, 35, 45, 51, 65, 83, 111 |
15 | 19, 49, 51, 55, 61, 75, 81, 115, 121, 135 |
16 | 15, 17, 39, 57, 87, 89, 99, 113, 117, 123 |
17 | 1, 9 13, 31, 49, 61, 63, 85, 91, 99 |
18 | 5, 11, 17, 23, 33, 35, 41, 65, 75, 93 |
19 | 1, 19, 27, 31, 45, 57, 67, 69, 85, 87 |
20 | 3, 5 17, 27, 59, 69, 129, 143, 153, 185 |
21 | 9, 19, 21, 55, 61, 69, 105, 111, 121, 129 |
22 | 3, 17, 27, 33, 57, 87, 105, 113, 117, 123 |
23 | 15, 21, 27, 37, 61, 69, 135, 147, 157, 159 |
24 | 3, 17, 33, 63, 75, 77, 89, 95, 117, 167 |
25 | 39, 49, 61, 85, 91, 115, 141, 159, 165, 183 |
26 | 5, 27, 45, 87, 101, 107, 111, 117, 125, 135 |
27 | 39, 79, 111, 115, 135, 187, 199, 219, 231, 235 |
28 | 57, 89, 95, 119, 125, 143, 165, 183, 213, 273 |
29 | 3, 33, 43, 63, 73, 75, 93, 99, 121, 133 |
30 | 35, 41, 83, 101, 105, 107, 135, 153, 161, 173 |
31 | 1, 19, 61, 69, 85, 99, 105, 151, 159, 171 |
32 | 5, 17, 65, 99, 107, 135, 153, 185, 209, 267 |
33 | 9, 25, 49, 79, 105, 285, 301, 303, 321, 355 |
34 | 41, 77, 113, 131, 143, 165, 185, 207, 227, 281 |
35 | 31, 49, 61, 69, 79, 121, 141, 247, 309, 325 |
36 | 5, 17, 23, 65, 117, 137, 159, 173, 189, 233 |
37 | 25, 31, 45, 69, 123, 141, 199, 201, 351, 375 |
38 | 45, 87, 107, 131, 153, 185, 191, 227, 231, 257 |
39 | 7, 19, 67, 91, 135, 165, 219, 231, 241, 301 |
40 | 87, 167, 195, 203, 213, 285, 293, 299, 389, 437 |
41 | 21, 31, 55, 63, 73, 75, 91, 111, 133, 139 |
42 | 11, 17, 33, 53, 65, 143, 161, 165, 215, 227 |
43 | 57, 67, 117, 175, 255, 267, 291, 309, 319, 369 |
44 | 17, 117, 119, 129, 143, 149, 287, 327, 359, 377 |
45 | 55, 69, 81, 93, 121, 133, 139, 159, 193, 229 |
46 | 21, 57, 63, 77, 167, 197, 237, 287, 305, 311 |
47 | 115, 127, 147, 279, 297, 339, 435, 541, 619, 649 |
48 | 59, 65, 89, 93, 147, 165, 189, 233, 243, 257 |
49 | 81, 111, 123, 139, 181, 201, 213, 265, 283, 339 |
50 | 27, 35, 51, 71, 113, 117, 131, 161, 195, 233 |
51 | 129, 139, 165, 231, 237, 247, 355, 391, 397, 439 |
52 | 47, 143, 173, 183, 197, 209, 269, 285, 335, 395 |
53 | 111, 145, 231, 265, 315, 339, 343, 369, 379, 421 |
54 | 33, 53, 131, 165, 195, 245, 255, 257, 315, 327 |
55 | 55, 67, 99, 127, 147, 169, 171, 199, 207, 267 |
56 | 5, 27, 47, 57, 89, 93, 147, 177, 189, 195 |
57 | 13, 25, 49, 61, 69, 111, 195, 273, 363, 423 |
58 | 27, 57, 63, 137, 141, 147, 161, 203, 213, 251 |
59 | 55, 99, 225, 427, 517, 607, 649, 687, 861, 871 |
60 | 93, 107, 173, 179, 257, 279, 369, 395, 399, 453 |
61 | 1, 31, 45, 229, 259, 283, 339, 391, 403, 465 |
62 | 57, 87, 117, 143, 153, 167, 171, 195, 203, 273 |
63 | 25, 165, 259, 301, 375, 387, 391, 409, 457, 471 |
64 | 59, 83, 95, 179, 189, 257, 279, 323, 353, 363 |
65 | 49, 79, 115, 141, 163, 229, 301, 345, 453, 493 |
66 | 5, 45, 173, 203, 275, 297, 387, 401, 443, 495 |
67 | 19, 31, 49, 57, 61, 75, 81, 165, 181, 237 |
68 | 23, 83, 125, 147, 149, 167, 285, 315, 345, 357 |
69 | 19, 91, 93, 103, 129, 153, 165, 201, 255, 385 |
70 | 35, 71, 167, 215, 263, 267, 273, 447, 473, 585 |
71 | 231, 325, 411, 435, 441, 465, 559, 577, 601, 721 |
72 | 93, 107, 129, 167, 249, 269, 329, 347, 429, 473 |
73 | 69, 181, 199, 273, 319, 433, 475, 501, 523, 645 |
74 | 35, 45, 57, 135, 153, 237, 257, 275, 461, 465 |
75 | 97, 207, 231, 271, 279, 289, 325, 381, 409, 427 |
76 | 15, 63, 117, 123, 143, 189, 215, 267, 285, 347 |
77 | 33, 43, 145, 163, 195, 261, 295, 379, 433, 451 |
78 | 11, 95, 111, 123, 147, 153, 191, 263, 303, 507 |
79 | 67, 199, 249, 277, 355, 367, 405, 447, 477, 511 |
80 | 65, 93, 117, 143, 285, 317, 549, 645, 765, 933 |
81 | 51, 63, 163, 205, 333, 349, 429, 433, 481, 553 |
82 | 57, 113, 185, 315, 363, 365, 375, 453, 623, 635 |
83 | 55, 97, 117, 121, 139, 285, 307, 405, 429, 561 |
84 | 35, 69, 213, 215, 333, 399, 525, 563, 587, 597 |
85 | 19, 61, 181, 295, 411, 433, 469, 519, 531, 823 |
86 | 35, 41, 65, 71, 113, 255, 261, 293, 357, 461 |
87 | 67, 129, 181, 195, 201, 217, 261, 277, 289, 339 |
88 | 299, 455, 483, 563, 605, 719, 735, 743, 753, 797 |
89 | 1, 21, 31, 49, 69, 99, 103, 265, 321, 441 |
90 | 33, 41, 53, 75, 227, 263, 273, 291, 297, 317 |
91 | 45, 81, 111, 201, 315, 339, 567, 619, 655, 771 |
92 | 83, 149, 197, 317, 363, 419, 485, 497, 519, 537 |
93 | 25, 51, 79, 105, 273, 405, 489, 553, 571, 579 |
94 | 3, 11, 105, 173, 273, 297, 321, 395, 407, 431 |
95 | 15, 37, 211, 339, 387, 415, 441, 447, 555, 561 |
96 | 17, 87, 93, 147, 165, 189, 237, 243, 315, 347 |
97 | 141, 165, 349, 399, 453, 595, 729, 741, 859, 885 |
98 | 51, 65, 107, 117, 141, 227, 273, 363, 471, 525 |
99 | 115, 145, 247, 319, 381, 427, 675, 717, 1207, 1231 |
100 | 15, 99, 153, 183, 267, 285, 357, 479, 603, 833 |
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