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