Primes just less than a power of two 301-400 bits  (Another of the Prime Pages' resources)
 New record prime (GIMPS): 282,589,933-1 with 24,862,048 digits by P. Laroche, G. Woltman, A. Blosser, et al. (7 Dec 2018).
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.
300 153, 185, 383, 413, 483, 539, 693, 779, 1047, 1097
301 265, 523, 861, 1249, 1299, 1309, 1365, 1869, 1963, 1981
302 267, 293, 647, 1043, 1307, 1581, 1601, 2037, 2141, 2241
303 121, 207, 241, 249, 321, 381, 549, 637, 835, 955
304 75, 1403, 1685, 1707, 1739, 1883, 1937, 2219, 2255, 2307
305 103, 429, 453, 1195, 1339, 1581, 2019, 2581, 2989, 3043
306 503, 947, 1017, 1797, 2063, 2093, 2175, 2597, 2655, 2817
307 99, 147, 187, 255, 319, 369, 511, 631, 879, 1021
308 159, 189, 615, 777, 959, 1025, 1079, 1139, 1409, 1443
309 493, 2673, 2733, 2949, 3243, 3525, 3595, 3799, 3969, 4051
310 77, 255, 635, 645, 755, 1097, 1127, 1235, 1377, 1533
311 45, 75, 181, 199, 271, 297, 471, 789, 885, 1071
312 203, 689, 753, 1385, 1449, 1547, 1575, 1655, 1683, 1799
313 139, 343, 439, 669, 675, 759, 915, 1893, 1993, 2371
314 113, 453, 677, 695, 981, 1013, 1037, 1067, 1121, 1277
315 465, 691, 1041, 1417, 1479, 1515, 1795, 2217, 2769, 2839
316 57, 243, 267, 293, 353, 399, 507, 899, 1259, 1323
317 33, 379, 523, 609, 1009, 1065, 1351, 1521, 1773, 1821
318 165, 275, 681, 807, 1337, 1427, 1617, 1931, 2075, 2295
319 795, 865, 1191, 1911, 2059, 2475, 2989, 3435, 3855, 4045
320 197, 743, 825, 843, 873, 1007, 1017, 1217, 1815, 2955
321 9, 45, 609, 769, 1053, 1165, 1389, 1395, 1431, 1675
322 11, 185, 923, 1121, 1233, 1307, 2307, 2373, 2583, 2717
323 141, 247, 309, 919, 1269, 1345, 1431, 1629, 1731, 1951
324 23, 177, 777, 923, 1055, 1299, 1329, 1385, 1449, 1799
325 399, 433, 1051, 1219, 1261, 1485, 1701, 2013, 2349, 2413
326 101, 117, 215, 731, 1731, 1823, 1833, 1995, 2603, 2807
327 595, 951, 979, 1077, 1297, 1549, 1939, 2667, 2961, 3055
328 155, 437, 629, 693, 843, 977, 1019, 1119, 1475, 1503
329 139, 243, 273, 339, 489, 531, 1665, 1963, 2145, 2343
330 255, 437, 927, 1001, 1217, 1445, 1595, 1911, 3185, 3435
331 61, 459, 745, 969, 1261, 1449, 1599, 1771, 2029, 2737
332 707, 1077, 1109, 1217, 1293, 1485, 1487, 1613, 2789, 2987
333 483, 741, 805, 913, 955, 1041, 1083, 1131, 1243, 1353
334 243, 603, 711, 981, 1085, 1425, 1637, 1901, 1953, 2423
335 321, 511, 541, 759, 871, 1227, 1399, 1821, 2131, 2337
336 3, 17, 303, 585, 627, 707, 723, 1047, 1413, 1479
337 75, 1443, 1579, 1615, 1659, 1693, 1741, 1785, 1915, 2793
338 15, 275, 315, 401, 467, 603, 623, 843, 951, 1053
339 147, 415, 751, 865, 901, 921, 1311, 1375, 1881, 1911
340 293, 299, 437, 699, 1187, 1203, 1209, 1217, 1389, 1439
341 229, 631, 765, 861, 951, 1071, 1101, 1203, 1263, 1503
342 65, 237, 263, 317, 707, 1017, 1085, 1353, 1517, 1755
343 199, 291, 495, 501, 561, 589, 691, 841, 915, 1377
344 119, 219, 527, 569, 617, 845, 993, 1079, 1107, 1253
345 475, 493, 859, 951, 1083, 1113, 1521, 2425, 2443, 2491
346 45, 57, 197, 363, 407, 1467, 1565, 1601, 1623, 1995
347 211, 367, 451, 1065, 1417, 1455, 1507, 1659, 1777, 2109
348 117, 143, 257, 359, 629, 759, 1085, 1295, 1469, 1533
349 285, 433, 579, 673, 859, 895, 1009, 2071, 2175, 2419
350 113, 131, 401, 425, 513, 555, 923, 1097, 1461, 2073
351 61, 135, 291, 429, 691, 1159, 2139, 2155, 2901, 3517
352 657, 879, 963, 999, 1263, 1305, 1323, 1439, 1449, 1865
353 139, 489, 523, 595, 621, 735, 1029, 1489, 1879, 1951
354 153, 251, 525, 537, 573, 783, 1371, 1563, 1605, 1691
355 49, 369, 589, 717, 957, 1221, 1609, 2185, 2197, 2355
356 173, 227, 393, 759, 803, 855, 989, 1385, 1497, 1623
357 243, 541, 739, 1033, 1075, 1105, 1621, 1725, 2575, 2739
358 671, 1005, 1161, 1211, 1247, 1365, 1491, 1793, 2681, 2957
359 411, 855, 901, 925, 1275, 1791, 2179, 2277, 2995, 3027
360 719, 1155, 1307, 1515, 1785, 1823, 2117, 2207, 2345, 2669
361 369, 663, 1779, 2539, 2691, 2793, 3501, 3751, 3909, 4173
362 605, 663, 1073, 1563, 1571, 1955, 2297, 2327, 2385, 2553
363 75, 97, 105, 111, 1287, 2251, 2341, 2391, 2481, 2511
364 923, 1239, 1653, 1725, 1917, 1949, 2009, 2045, 2339, 2609
365 169, 261, 295, 325, 369, 493, 639, 723, 2079, 2241
366 167, 507, 635, 657, 747, 837, 1115, 1511, 1785, 1787
367 487, 801, 1279, 1407, 1509, 1827, 2365, 2409, 2467, 3049
368 315, 419, 785, 1139, 1289, 1953, 2567, 2595, 2799, 3107
369 25, 195, 445, 825, 1339, 1551, 1599, 1729, 1869, 1959
370 495, 813, 1797, 1977, 2001, 2063, 2303, 2315, 2505, 2913
371 741, 747, 925, 1077, 1485, 1647, 1815, 2115, 2305, 2319
372 177, 207, 563, 797, 1749, 1997, 2247, 2475, 2615, 2873
373 333, 489, 735, 843, 1813, 2295, 2491, 3189, 3513, 3519
374 65, 153, 371, 495, 855, 987, 1433, 1983, 2235, 2247
375 679, 979, 1089, 1119, 1669, 1767, 2065, 2547, 2635, 2697
376 57, 473, 519, 629, 1035, 1239, 1929, 2085, 2237, 2985
377 259, 321, 511, 663, 1485, 1693, 1791, 2253, 2409, 2553
378 417, 447, 825, 1991, 2207, 2693, 2993, 3101, 3177, 3287
379 19, 99, 319, 355, 679, 711, 795, 925, 1069, 1455
380 65, 483, 677, 723, 1133, 1139, 1175, 1263, 1347, 1469
381 313, 735, 1203, 2209, 2629, 3033, 3055, 3091, 3315, 4003
382 105, 227, 635, 677, 963, 1083, 1641, 2085, 2243, 2411
383 31, 187, 367, 421, 471, 567, 607, 747, 1035, 1699
384 317, 1437, 1557, 1617, 2147, 2319, 2729, 3087, 3093, 3273
385 265, 1215, 1911, 2005, 2101, 2401, 2449, 2455, 2565, 2679
386 231, 747, 881, 923, 1287, 1611, 2493, 2735, 2837, 3633
387 615, 621, 795, 919, 1021, 1111, 1255, 1287, 1689, 2095
388 45, 63, 269, 347, 483, 525, 717, 837, 875, 959
389 21, 51, 103, 313, 843, 871, 883, 1141, 1179, 1743
390 137, 293, 383, 461, 1017, 1283, 1773, 2057, 2693, 3047
391 105, 127, 399, 645, 675, 1671, 1791, 2085, 2227, 2275
392 107, 299, 623, 1035, 1389, 1437, 1589, 1827, 2285, 2607
393 93, 331, 549, 1113, 1411, 2523, 2551, 2719, 3393, 4291
394 377, 447, 987, 1161, 1497, 1571, 2043, 2187, 2303, 2615
395 531, 1137, 2161, 2205, 2215, 2907, 3055, 3151, 3481, 3655
396 605, 695, 909, 945, 1229, 1365, 1997, 2397, 2837, 3285
397 81, 463, 673, 1071, 1165, 1425, 1905, 1999, 2061, 2133
398 131, 231, 777, 951, 1457, 1547, 1673, 1893, 2145, 2241
399 91, 219, 937, 1731, 2749, 2875, 3201, 3489, 3729, 4149
400 593, 663, 767, 879, 1205, 2457, 3107, 3195, 3263, 3267

 Another prime page by Chris K. Caldwell