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unprimeable numbers
A number that cannot be turned into a prime by changing a single digit. more

The first 600 unprimeable numbers :
200, 204, 206, 208, 320, 322, 324, 325, 326, 328, 510, 512, 514, 515, 516, 518, 530, 532, 534, 535, 536, 538, 620, 622, 624, 625, 626, 628, 840, 842, 844, 845, 846, 848, 890, 892, 894, 895, 896, 898, 1070, 1072, 1074, 1075, 1076, 1078, 1130, 1132, 1134, 1135, 1136, 1138, 1140, 1142, 1144, 1145, 1146, 1148, 1260, 1262, 1264, 1265, 1266, 1268, 1330, 1332, 1334, 1335, 1336, 1338, 1340, 1342, 1344, 1345, 1346, 1348, 1350, 1352, 1354, 1355, 1356, 1358, 1410, 1412, 1414, 1415, 1416, 1418, 1460, 1462, 1464, 1465, 1466, 1468, 1500, 1502, 1504, 1505, 1506, 1508, 1640, 1642, 1644, 1645, 1646, 1648, 1670, 1672, 1674, 1675, 1676, 1678, 1680, 1682, 1684, 1685, 1686, 1688, 1710, 1712, 1714, 1715, 1716, 1718, 1760, 1762, 1764, 1765, 1766, 1768, 1790, 1792, 1794, 1795, 1796, 1798, 1850, 1852, 1854, 1855, 1856, 1858, 1890, 1892, 1894, 1895, 1896, 1898, 1920, 1922, 1924, 1925, 1926, 1928, 1960, 1962, 1964, 1965, 1966, 1968, 2040, 2042, 2044, 2045, 2046, 2048, 2070, 2072, 2074, 2075, 2076, 2078, 2100, 2102, 2104, 2105, 2106, 2108, 2180, 2182, 2184, 2185, 2186, 2188, 2190, 2192, 2194, 2195, 2196, 2198, 2320, 2322, 2324, 2325, 2326, 2328, 2360, 2362, 2364, 2365, 2366, 2368, 2400, 2402, 2404, 2405, 2406, 2408, 2480, 2482, 2484, 2485, 2486, 2488, 2490, 2492, 2494, 2495, 2496, 2498, 2510, 2512, 2514, 2515, 2516, 2518, 2560, 2562, 2564, 2565, 2566, 2568, 2580, 2582, 2584, 2585, 2586, 2588, 2820, 2822, 2824, 2825, 2826, 2828, 2940, 2942, 2944, 2945, 2946, 2948, 2980, 2982, 2984, 2985, 2986, 2988, 3050, 3052, 3054, 3055, 3056, 3058, 3090, 3092, 3094, 3095, 3096, 3098, 3140, 3142, 3144, 3145, 3146, 3148, 3150, 3152, 3154, 3155, 3156, 3158, 3170, 3172, 3174, 3175, 3176, 3178, 3230, 3232, 3234, 3235, 3236, 3238, 3240, 3242, 3244, 3245, 3246, 3248, 3260, 3262, 3264, 3265, 3266, 3268, 3280, 3282, 3284, 3285, 3286, 3288, 3420, 3422, 3424, 3425, 3426, 3428, 3470, 3472, 3474, 3475, 3476, 3478, 3480, 3482, 3484, 3485, 3486, 3488, 3500, 3502, 3504, 3505, 3506, 3508, 3560, 3562, 3564, 3565, 3566, 3568, 3660, 3662, 3664, 3665, 3666, 3668, 3680, 3682, 3684, 3685, 3686, 3688, 3740, 3742, 3744, 3745, 3746, 3748, 3750, 3752, 3754, 3755, 3756, 3758, 3780, 3782, 3784, 3785, 3786, 3788, 3810, 3812, 3814, 3815, 3816, 3818, 3890, 3892, 3894, 3895, 3896, 3898, 3950, 3952, 3954, 3955, 3956, 3958, 3970, 3972, 3974, 3975, 3976, 3978, 3990, 3992, 3994, 3995, 3996, 3998, 4030, 4032, 4034, 4035, 4036, 4038, 4060, 4062, 4064, 4065, 4066, 4068, 4080, 4082, 4084, 4085, 4086, 4088, 4100, 4102, 4104, 4105, 4106, 4108, 4140, 4142, 4144, 4145, 4146, 4148, 4160, 4162, 4164, 4165, 4166, 4168, 4180, 4182, 4184, 4185, 4186, 4188, 4190, 4192, 4194, 4195, 4196, 4198, 4300, 4302, 4304, 4305, 4306, 4308, 4310, 4312, 4314, 4315, 4316, 4318, 4380, 4382, 4384, 4385, 4386, 4388, 4410, 4412, 4414, 4415, 4416, 4418, 4430, 4432, 4434, 4435, 4436, 4438, 4470, 4472, 4474, 4475, 4476, 4478, 4530, 4532, 4534, 4535, 4536, 4538, 4550, 4552, 4554, 4555, 4556, 4558, 4570, 4572, 4574, 4575, 4576, 4578, 4610, 4612, 4614, 4615, 4616, 4618, 4680, 4682, 4684, 4685, 4686, 4688, 4710, 4712, 4714, 4715, 4716, 4718, 4740, 4742, 4744, 4745, 4746, 4748, 4760, 4762, 4764, 4765, 4766, 4768, 4770, 4772, 4774, 4775, 4776, 4778, 4820, 4822, 4824, 4825, 4826, 4828, 4840, 4842, 4844, 4845, 4846, 4848, 4850, 4852, 4854, 4855, 4856, 4858, 4890, 4892, 4894, 4895, 4896, 4898, 4920, 4922, 4924, 4925, 4926, 4928, 5040, 5042, 5044, 5045, 5046, 5048, 5060, 5062, 5064, 5065, 5066, 5068, 5120, 5122, 5124, 5125, 5126, 5128, 5130, 5132, 5134, 5135, 5136, 5138, 5210, 5212, 5214, 5215, 5216, 5218, 5240, 5242.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 2855169 values, from 200 to 10000000).

n\r 0  1 
22379258475911 2 
38673619516161036192 3 
411897382380561189520237855 4 
5951696475871475855475872475875 5 
6765006186724849360102355764892186832 6 
7401474401592401513401461416351416452416326 7 
8595038118862594791118891594700119194594729118964 8 
9289183317224345364289048317256345409289130317136345419 9 
1047585517475841184758544758414758541447585421 10 
11239143267235257771257854267087258071257827257744267335248417276685

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.