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Ruth-Aaron pair  and  unprimeable n.

First numbers that belong to both sets:

1330, 1682, 2108, 2492, 3248, 4185, 4186, 4192, 5960, 6812, 8855, 8856, 10648, 12352, 13775, 13776, 14588, 17080, 18655, 18656, 20450, 24895, 24896, 26650, 35456, 37828, 42624, 42625, 43215, 43216, 43680, 48204, 49240, 61760, 68950, 99164, 106894, 118656, 128774, 128775, 132210, 141340, 148215, 148216, 172774, 173162, 183446, 189080, 216294, 235586, 261020, 268656, 268715, 268716, 304325, 304326, 329988, 350600, 370348, 373704, 380438, 380964, 381728, 394855, 394856, 416120, 421820, 436932, 441212, 453474, 453475, 461824, 461825, 467302, 470120, 488976, 493922, 501830, 509852, 529194, 529195, 550032, 554682, 563390, 565824, 572015, 572016, 576984, 576985, 598250, 608316, 618752, 639848, 665322, 667628, 685228, 694430, 732088, 740726, 742854, 748230, 821272, 839375, 839376, 842128, 849375, 849376, 850746, 851710, 856608, 859408, 861400, 890724, 909624, 909625, 911538, 944108, 956040, 959582, 961572, 962140, 965095, 965096, 976375, 976376, 977280, 977778, 999072, 1039888, 1045950, 1054828, 1084288, 1100280, 1104264, 1131812, 1166068, 1172948, 1173148, 1173504, 1173505, 1199988, 1232746, 1236600, 1240965, 1240966, 1243500, 1246932, 1252096, 1252510, 1261008, 1263680, 1267920, 1293140, 1302092, 1315976, 1330406, 1330448, 1330895, 1330896, 1351272, 1361070, 1376110, 1379908, 1386536, 1459864, 1474375, 1474376, 1492032, 1496550, 1497465, 1497466, 1512412, 1516788, 1517450, 1560500, 1562092, 1570280, 1572176, 1607045, 1607046, 1618788, 1672710, 1686750, 1686894, 1711142, 1777026, 1797112, 1799940, 1801162, 1809710, 1838184, 1864056, 1915578, 1926235, 1926236, 1942280, 1943404, 1962796, 1967765, 1967766, 2009350, 2020800, 2022344, 2029948, 2040752, 2042950, 2045976, 2049318, 2067890, 2114435, 2114436, 2128984, 2128985, 2138172, 2138928, 2260588, 2373452, 2387375, 2387376, 2390482, 2407320, 2442185, 2442186, 2493800, 2527020, 2538534, 2579308, 2586234, 2586235, 2649042, 2701656, 2742395, 2742396, 2744288, 2778560, 2802298, 2834766, 2849042, 2854740, 2872492, 2991418, 3002296, 3009412, 3046742, 3069206, 3161664, 3161665, 3198042, 3223788, 3230074, 3265805, 3265806, 3394015, 3394016, 3423436, 3457496, 3476964, 3476965, 3481352, 3524496, 3584195, 3584196, 3594245, 3594246, 3668588, 3672500, 3703588, 3743350, 3749428, 3835132, 3897530, 3912336, 3975060, 4055618, 4057122, 4076328, 4082816, 4086226, 4091402, 4124538.

Some larger examples :