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interprime numbers
A composite that is the average of two consecutive primes. more

The first 600 interprime numbers :
4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99, 102, 105, 108, 111, 120, 129, 134, 138, 144, 150, 154, 160, 165, 170, 176, 180, 186, 192, 195, 198, 205, 217, 225, 228, 231, 236, 240, 246, 254, 260, 266, 270, 274, 279, 282, 288, 300, 309, 312, 315, 324, 334, 342, 348, 351, 356, 363, 370, 376, 381, 386, 393, 399, 405, 414, 420, 426, 432, 436, 441, 446, 453, 459, 462, 465, 473, 483, 489, 495, 501, 506, 515, 522, 532, 544, 552, 560, 566, 570, 574, 582, 590, 596, 600, 604, 610, 615, 618, 625, 636, 642, 645, 650, 656, 660, 667, 675, 680, 687, 696, 705, 714, 723, 730, 736, 741, 747, 754, 759, 765, 771, 780, 792, 803, 810, 816, 822, 825, 828, 834, 846, 855, 858, 861, 870, 879, 882, 885, 897, 909, 915, 924, 933, 939, 944, 950, 960, 969, 974, 980, 987, 994, 1003, 1011, 1016, 1020, 1026, 1032, 1036, 1044, 1050, 1056, 1062, 1066, 1078, 1089, 1092, 1095, 1100, 1106, 1113, 1120, 1126, 1140, 1152, 1158, 1167, 1176, 1184, 1190, 1197, 1207, 1215, 1220, 1226, 1230, 1234, 1243, 1254, 1268, 1278, 1281, 1286, 1290, 1294, 1299, 1302, 1305, 1313, 1320, 1324, 1344, 1364, 1370, 1377, 1390, 1404, 1416, 1425, 1428, 1431, 1436, 1443, 1449, 1452, 1456, 1465, 1476, 1482, 1485, 1488, 1491, 1496, 1505, 1517, 1527, 1537, 1546, 1551, 1556, 1563, 1569, 1575, 1581, 1590, 1599, 1604, 1608, 1611, 1616, 1620, 1624, 1632, 1647, 1660, 1665, 1668, 1681, 1695, 1698, 1704, 1715, 1722, 1728, 1737, 1744, 1750, 1756, 1768, 1780, 1785, 1788, 1795, 1806, 1817, 1827, 1839, 1854, 1864, 1869, 1872, 1875, 1878, 1884, 1895, 1904, 1910, 1922, 1932, 1941, 1950, 1962, 1976, 1983, 1990, 1995, 1998, 2001, 2007, 2014, 2022, 2028, 2034, 2046, 2058, 2066, 2075, 2082, 2085, 2088, 2094, 2105, 2112, 2121, 2130, 2134, 2139, 2142, 2148, 2157, 2170, 2191, 2205, 2210, 2217, 2229, 2238, 2241, 2247, 2259, 2268, 2271, 2277, 2284, 2290, 2295, 2303, 2310, 2322, 2336, 2340, 2344, 2349, 2354, 2364, 2374, 2379, 2382, 2386, 2391, 2396, 2405, 2414, 2420, 2430, 2439, 2444, 2453, 2463, 2470, 2475, 2490, 2512, 2526, 2535, 2541, 2546, 2550, 2554, 2568, 2585, 2592, 2601, 2613, 2619, 2627, 2640, 2652, 2658, 2661, 2667, 2674, 2680, 2685, 2688, 2691, 2696, 2703, 2709, 2712, 2716, 2724, 2730, 2736, 2745, 2751, 2760, 2772, 2783, 2790, 2794, 2799, 2802, 2811, 2826, 2835, 2840, 2847, 2854, 2859, 2870, 2883, 2892, 2900, 2906, 2913, 2922, 2933, 2946, 2955, 2960, 2966, 2970, 2985, 3000, 3006, 3015, 3021, 3030, 3039, 3045, 3055, 3064, 3073, 3081, 3086, 3099, 3114, 3120, 3129, 3150, 3165, 3168, 3175, 3184, 3189, 3197, 3206, 3213, 3219, 3225, 3240, 3252, 3255, 3258, 3265, 3285, 3300, 3304, 3310, 3316, 3321, 3326, 3330, 3337, 3345, 3353, 3360, 3366, 3372, 3381, 3390, 3399, 3410, 3423, 3441, 3453, 3459, 3462, 3465, 3468, 3480, 3495, 3505, 3514, 3522, 3528, 3531, 3536, 3540, 3544, 3552, 3558, 3565, 3576, 3582, 3588, 3600, 3610, 3615, 3620, 3627, 3634, 3640, 3651, 3665, 3672, 3675, 3684, 3694, 3699, 3705, 3714, 3723, 3730, 3736, 3750, 3764, 3768, 3774, 3786, 3795, 3800, 3812, 3822, 3828, 3840, 3849, 3852, 3858, 3870, 3879, 3885, 3898, 3909, 3914, 3918, 3921, 3926, 3930, 3937, 3945, 3957, 3978, 3995, 4002, 4005, 4010, 4016, 4020, 4024, 4038, 4050, 4054, 4065, 4076, 4085, 4092, 4096, 4105, 4119, 4128, 4131, 4136, 4146, 4155, 4158, 4168, 4189, 4206, 4214, 4218, 4224, 4230, 4236, 4242, 4248, 4256, 4260, 4266, 4272, 4278, 4286, 4293, 4312, 4332, 4338, 4344, 4353, 4360, 4368, 4382, 4394, 4403, 4415, 4422.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 5761454 values, from 4 to 99999998).

n\r 0  1 
232063622555092 2 
3323294012640481264466 3 
41603640127783016027221277262 4 
515838031070648101846010183691070174 5 
616821935023527624731550747761696501993 6 
71026824811622787232768553768380787173811670 7 
8800124638069801644638797803516639761801078638465 8 
9107642142099242149710780924213064218591078427421750421110 9 
10838393438302551759466606632101745410632346466701551763438073 10 
11604209532728523993491728529614500379500714529822491558523629533080

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.