A semiprime whose digital reverse is a different semiprime. more
The first 600 emirpimeses :
15,
26,
39,
49,
51,
58,
62,
85,
93,
94,
115,
122,
123,
129,
143,
155,
158,
159,
169,
177,
178,
183,
185,
187,
203,
205,
221,
226,
265,
289,
302,
314,
319,
321,
326,
327,
329,
335,
339,
341,
355,
381,
394,
398,
413,
415,
437,
493,
497,
502,
511,
514,
533,
538,
551,
553,
559,
562,
581,
586,
589,
622,
623,
629,
667,
685,
718,
723,
734,
766,
771,
781,
794,
817,
835,
851,
871,
893,
899,
913,
921,
923,
926,
933,
951,
955,
961,
982,
985,
998,
1006,
1011,
1027,
1041,
1043,
1046,
1047,
1057,
1059,
1067,
1079,
1101,
1115,
1119,
1121,
1135,
1137,
1141,
1145,
1149,
1154,
1165,
1169,
1174,
1177,
1195,
1202,
1211,
1214,
1219,
1234,
1238,
1243,
1247,
1253,
1273,
1286,
1293,
1299,
1306,
1313,
1315,
1317,
1318,
1322,
1343,
1346,
1347,
1354,
1357,
1366,
1371,
1379,
1382,
1383,
1387,
1401,
1402,
1405,
1411,
1415,
1417,
1418,
1437,
1438,
1454,
1461,
1466,
1469,
1497,
1502,
1507,
1513,
1514,
1527,
1538,
1561,
1563,
1569,
1577,
1623,
1641,
1642,
1651,
1655,
1658,
1671,
1679,
1687,
1691,
1703,
1706,
1707,
1714,
1717,
1727,
1731,
1735,
1754,
1757,
1761,
1765,
1766,
1769,
1774,
1779,
1795,
1797,
1807,
1814,
1817,
1843,
1849,
1874,
1882,
1891,
1893,
1894,
1897,
1903,
1915,
1923,
1927,
1937,
1942,
1961,
1969,
1981,
1983,
1985,
2018,
2021,
2041,
2042,
2047,
2051,
2059,
2062,
2066,
2077,
2098,
2206,
2219,
2231,
2234,
2245,
2257,
2258,
2263,
2279,
2402,
2413,
2426,
2429,
2435,
2443,
2446,
2449,
2458,
2461,
2462,
2474,
2479,
2491,
2495,
2602,
2603,
2605,
2614,
2627,
2642,
2654,
2669,
2807,
2815,
2818,
2831,
2839,
2845,
2855,
2878,
2881,
3007,
3013,
3043,
3046,
3047,
3053,
3062,
3063,
3065,
3071,
3085,
3091,
3093,
3097,
3098,
3099,
3103,
3106,
3117,
3131,
3134,
3139,
3142,
3151,
3153,
3155,
3166,
3173,
3189,
3197,
3199,
3207,
3215,
3227,
3247,
3261,
3291,
3305,
3309,
3317,
3326,
3327,
3334,
3338,
3365,
3385,
3401,
3403,
3415,
3418,
3419,
3421,
3431,
3437,
3442,
3446,
3453,
3455,
3459,
3473,
3481,
3503,
3505,
3513,
3518,
3521,
3543,
3554,
3563,
3579,
3589,
3599,
3603,
3622,
3629,
3635,
3639,
3646,
3647,
3651,
3653,
3665,
3667,
3669,
3679,
3687,
3693,
3694,
3695,
3707,
3713,
3715,
3721,
3737,
3743,
3754,
3777,
3778,
3785,
3809,
3814,
3817,
3826,
3831,
3839,
3866,
3869,
3891,
3893,
3898,
3899,
3903,
3921,
3946,
3949,
3957,
3958,
3959,
3963,
3979,
3981,
3983,
3985,
3986,
4109,
4115,
4117,
4121,
4135,
4138,
4145,
4151,
4162,
4166,
4171,
4174,
4178,
4181,
4183,
4187,
4195,
4198,
4307,
4309,
4313,
4319,
4321,
4322,
4333,
4369,
4385,
4387,
4399,
4511,
4531,
4535,
4537,
4538,
4541,
4553,
4555,
4562,
4571,
4573,
4574,
4577,
4579,
4594,
4711,
4714,
4727,
4735,
4742,
4754,
4765,
4771,
4781,
4907,
4954,
4955,
4963,
4981,
5006,
5033,
5041,
5053,
5062,
5078,
5086,
5095,
5111,
5114,
5123,
5131,
5141,
5143,
5155,
5165,
5173,
5177,
5182,
5191,
5311,
5314,
5317,
5318,
5327,
5329,
5339,
5342,
5345,
5354,
5359,
5363,
5366,
5371,
5374,
5378,
5386,
5398,
5411,
5414,
5422,
5426,
5435,
5438,
5447,
5455,
5458,
5465,
5482,
5498,
5509,
5513,
5515,
5539,
5543,
5545,
5554,
5561,
5567,
5579,
5582,
5585,
5587,
5594,
5603,
5606,
5611,
5615,
5617,
5627,
5633,
5645,
5663,
5671,
5674,
5677,
5686,
5699,
5803,
5806,
5818,
5833,
5834,
5855,
5873,
5891,
5893,
5899,
5905,
5911,
5914,
5917,
5926,
5942,
5947,
5963,
5971,
5977,
5989,
5999,
6001,
6005,
6013,
6022,
6031,
6038,
6046,
6049,
6065,
6071,
6077,
6085,
6209,
6227,
6233,
6239,
6242,
6245,
6283,
6295,
6401,
6403,
6406,
6418,
6431,
6437,
6439,
6442,
6443,
6458,
6463,
6467,
6487,
6493,
6499,
6602,
6613,
6614,
6617,
6631,
6635,
6641,
6649,
6658,
6667,
6671.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 4320516 values, from 15 to 99999997).
n\r | 0 | 1 |
2 | 814281 | 3506235 | 2 |
3 | 237432 | 2041416 | 2041668 | 3 |
4 | 0 | 1752703 | 814281 | 1753532 | 4 |
5 | 344167 | 1023250 | 983156 | 996212 | 973731 | 5 |
6 | 0 | 1634516 | 407381 | 237432 | 406900 | 1634287 | 6 |
7 | 254237 | 676654 | 681018 | 675033 | 676873 | 676848 | 679853 | 7 |
8 | 0 | 876309 | 407447 | 875748 | 0 | 876394 | 406834 | 877784 | 8 |
9 | 0 | 680796 | 680468 | 118932 | 680494 | 681318 | 118500 | 680126 | 679882 | 9 |
10 | 0 | 820986 | 207372 | 795451 | 203884 | 344167 | 202264 | 775784 | 200761 | 769847 | 10 |
11 | 71290 | 425309 | 424431 | 424649 | 426232 | 424276 | 424276 | 425690 | 424333 | 424641 | 425389 |
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.