Search a number
Cunningham numbers
A number of the form bk ± 1 with b, k > 1 more

The first 600 Cunningham numbers :
3, 5, 7, 8, 9, 10, 15, 17, 24, 26, 28, 31, 33, 35, 37, 48, 50, 63, 65, 80, 82, 99, 101, 120, 122, 124, 126, 127, 129, 143, 145, 168, 170, 195, 197, 215, 217, 224, 226, 242, 244, 255, 257, 288, 290, 323, 325, 342, 344, 360, 362, 399, 401, 440, 442, 483, 485, 511, 513, 528, 530, 575, 577, 624, 626, 675, 677, 728, 730, 783, 785, 840, 842, 899, 901, 960, 962, 999, 1001, 1023, 1025, 1088, 1090, 1155, 1157, 1224, 1226, 1295, 1297, 1330, 1332, 1368, 1370, 1443, 1445, 1520, 1522, 1599, 1601, 1680, 1682, 1727, 1729, 1763, 1765, 1848, 1850, 1935, 1937, 2024, 2026, 2047, 2049, 2115, 2117, 2186, 2188, 2196, 2198, 2208, 2210, 2303, 2305, 2400, 2402, 2499, 2501, 2600, 2602, 2703, 2705, 2743, 2745, 2808, 2810, 2915, 2917, 3024, 3026, 3124, 3126, 3135, 3137, 3248, 3250, 3363, 3365, 3374, 3376, 3480, 3482, 3599, 3601, 3720, 3722, 3843, 3845, 3968, 3970, 4095, 4097, 4224, 4226, 4355, 4357, 4488, 4490, 4623, 4625, 4760, 4762, 4899, 4901, 4912, 4914, 5040, 5042, 5183, 5185, 5328, 5330, 5475, 5477, 5624, 5626, 5775, 5777, 5831, 5833, 5928, 5930, 6083, 6085, 6240, 6242, 6399, 6401, 6560, 6562, 6723, 6725, 6858, 6860, 6888, 6890, 7055, 7057, 7224, 7226, 7395, 7397, 7568, 7570, 7743, 7745, 7775, 7777, 7920, 7922, 7999, 8001, 8099, 8101, 8191, 8193, 8280, 8282, 8463, 8465, 8648, 8650, 8835, 8837, 9024, 9026, 9215, 9217, 9260, 9262, 9408, 9410, 9603, 9605, 9800, 9802, 9999, 10001, 10200, 10202, 10403, 10405, 10608, 10610, 10647, 10649, 10815, 10817, 11024, 11026, 11235, 11237, 11448, 11450, 11663, 11665, 11880, 11882, 12099, 12101, 12166, 12168, 12320, 12322, 12543, 12545, 12768, 12770, 12995, 12997, 13224, 13226, 13455, 13457, 13688, 13690, 13823, 13825, 13923, 13925, 14160, 14162, 14399, 14401, 14640, 14642, 14883, 14885, 15128, 15130, 15375, 15377, 15624, 15626, 15875, 15877, 16128, 16130, 16383, 16385, 16640, 16642, 16806, 16808, 16899, 16901, 17160, 17162, 17423, 17425, 17575, 17577, 17688, 17690, 17955, 17957, 18224, 18226, 18495, 18497, 18768, 18770, 19043, 19045, 19320, 19322, 19599, 19601, 19682, 19684, 19880, 19882, 20163, 20165, 20448, 20450, 20735, 20737, 21024, 21026, 21315, 21317, 21608, 21610, 21903, 21905, 21951, 21953, 22200, 22202, 22499, 22501, 22800, 22802, 23103, 23105, 23408, 23410, 23715, 23717, 24024, 24026, 24335, 24337, 24388, 24390, 24648, 24650, 24963, 24965, 25280, 25282, 25599, 25601, 25920, 25922, 26243, 26245, 26568, 26570, 26895, 26897, 26999, 27001, 27224, 27226, 27555, 27557, 27888, 27890, 28223, 28225, 28560, 28562, 28899, 28901, 29240, 29242, 29583, 29585, 29790, 29792, 29928, 29930, 30275, 30277, 30624, 30626, 30975, 30977, 31328, 31330, 31683, 31685, 32040, 32042, 32399, 32401, 32760, 32762, 32767, 32769, 33123, 33125, 33488, 33490, 33855, 33857, 34224, 34226, 34595, 34597, 34968, 34970, 35343, 35345, 35720, 35722, 35936, 35938, 36099, 36101, 36480, 36482, 36863, 36865, 37248, 37250, 37635, 37637, 38024, 38026, 38415, 38417, 38808, 38810, 39203, 39205, 39303, 39305, 39600, 39602, 39999, 40001, 40400, 40402, 40803, 40805, 41208, 41210, 41615, 41617, 42024, 42026, 42435, 42437, 42848, 42850, 42874, 42876, 43263, 43265, 43680, 43682, 44099, 44101, 44520, 44522, 44943, 44945, 45368, 45370, 45795, 45797, 46224, 46226, 46655, 46657, 47088, 47090, 47523, 47525, 47960, 47962, 48399, 48401, 48840, 48842, 49283, 49285, 49728, 49730, 50175, 50177, 50624, 50626, 50652, 50654, 51075, 51077, 51528, 51530, 51983, 51985, 52440, 52442, 52899, 52901, 53360, 53362, 53823, 53825, 54288, 54290, 54755, 54757, 54871, 54873, 55224, 55226, 55695, 55697, 56168, 56170, 56643, 56645, 57120, 57122, 57599, 57601, 58080, 58082, 58563, 58565, 59048, 59050, 59318, 59320, 59535, 59537, 60024, 60026, 60515, 60517, 61008, 61010, 61503, 61505, 62000, 62002, 62499, 62501, 63000, 63002, 63503, 63505, 63999, 64001, 64008, 64010, 64515, 64517, 65024, 65026, 65535, 65537, 66048, 66050, 66563, 66565, 67080.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 63447179 values, from 3 to 999999961946177).

n\r 0  1 
23172358731723592 2 
3211490581060826031689861 3 
415861794158617961586179315861796 4 
525338397636495412689437126894386364953 5 
61057452753041321584493210574531530412815844929 6 
791208341356717690779861807047334390782554532112 7 
8158364977956102158365007905694252977905694252937956102 8 
970939781057466970605237027540136702740370275403345517601935 9 
10126691963182475634471663447193182477126692013182479634472163447193182476 10 
11576862028930691151770957677511151728557677515767753182185767754186648642605

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.