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 |
2 | 3206362 | 2555092 | 2 |
3 | 3232940 | 1264048 | 1264466 | 3 |
4 | 1603640 | 1277830 | 1602722 | 1277262 | 4 |
5 | 1583803 | 1070648 | 1018460 | 1018369 | 1070174 | 5 |
6 | 1682193 | 502352 | 762473 | 1550747 | 761696 | 501993 | 6 |
7 | 1026824 | 811622 | 787232 | 768553 | 768380 | 787173 | 811670 | 7 |
8 | 800124 | 638069 | 801644 | 638797 | 803516 | 639761 | 801078 | 638465 | 8 |
9 | 1076421 | 420992 | 421497 | 1078092 | 421306 | 421859 | 1078427 | 421750 | 421110 | 9 |
10 | 838393 | 438302 | 551759 | 466606 | 632101 | 745410 | 632346 | 466701 | 551763 | 438073 | 10 |
11 | 604209 | 532728 | 523993 | 491728 | 529614 | 500379 | 500714 | 529822 | 491558 | 523629 | 533080 |
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.