# 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).

Pages: 8-100 bits, 101-200 bits, 201-300 bits, 301-400 bits
n ten least k's for which 2n-k is prime.
5, 15, 17, 23, 27, 29, 33, 45, 57, 59
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