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 |
2 | 2379258 | 475911 | 2 |
3 | 867361 | 951616 | 1036192 | 3 |
4 | 1189738 | 238056 | 1189520 | 237855 | 4 |
5 | 951696 | 475871 | 475855 | 475872 | 475875 | 5 |
6 | 765006 | 186724 | 849360 | 102355 | 764892 | 186832 | 6 |
7 | 401474 | 401592 | 401513 | 401461 | 416351 | 416452 | 416326 | 7 |
8 | 595038 | 118862 | 594791 | 118891 | 594700 | 119194 | 594729 | 118964 | 8 |
9 | 289183 | 317224 | 345364 | 289048 | 317256 | 345409 | 289130 | 317136 | 345419 | 9 |
10 | 475855 | 17 | 475841 | 18 | 475854 | 475841 | 475854 | 14 | 475854 | 21 | 10 |
11 | 239143 | 267235 | 257771 | 257854 | 267087 | 258071 | 257827 | 257744 | 267335 | 248417 | 276685 |
A pictorial representation of the table above
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.