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interprime n.  and  vampire n.

First numbers that belong to both sets:

1827, 108135, 116725, 124483, 126027, 150300, 152608, 186624, 215860, 233896, 241564, 263074, 286416, 312975, 319059, 341653, 475380, 489159, 538650, 736695, 815958, 841995, 10165815, 10192248, 10323225, 10723185, 10734192, 10796674, 11147836, 11148520, 11246890, 11293744, 11345229, 11479230, 11525490, 11541816, 11559960, 11682468, 11683512, 11690532, 11833645, 11908215, 11925540, 11926728, 11930170, 11948310, 12081960, 12083706, 12097350, 12213585, 12296740, 12387735, 12417993, 12419775, 12453012, 12459640, 12484057, 12492864, 12613990, 12640095, 12746650, 12752860, 12754075, 12762000, 12843000, 12883540, 12966480, 13104954, 13230369, 13241250, 13268772, 13350897, 13604350, 13754790, 13967820, 13982400, 14174370, 14245632, 14346072, 14637550, 14713650, 14720368, 14736780, 14739340, 15003000, 15085620, 15123960, 15206715, 15243390, 15261696, 15316938, 15384330, 15401628, 15487380, 15632478, 15812680, 15819300, 15842344, 15862063, 16254760, 16265088, 16335450, 16679520, 16789540, 16820005, 16825338, 16897482, 17138295, 17230360, 17265276, 17479300, 17586279, 17597943, 17650215, 17834593, 17932500, 18002997, 18208750, 18317520, 18398520, 18993316, 19052352, 19120500, 19202850, 19209190, 19315768, 19384596, 19736257, 20506248, 20579350, 20716965, 20837376, 21218575, 21275046, 21455280, 21597210, 21760398, 21799692, 21819334, 21826548, 22245664, 22336524, 22673196, 22877140, 23071149, 23237190, 23287176, 23497510, 23524141, 23559466, 23726592, 24156405, 24317500, 24539170, 24640528, 24674832, 24753190, 24916815, 25018420, 25149388, 25301727, 25510000, 25864398, 26164719, 26198073, 26391870, 26397184, 26432640, 26772624, 26805240, 26859375, 27315868, 27625455, 27693864, 27998275, 28173600, 28679904, 29067948, 29561454, 29739550, 29864718, 30183790, 30185946, 30857940, 31249872, 31427190, 31874193, 32294880, 32426892, 32499918, 32631984, 32682496, 32841900, 32898474, 33486390, 33669108, 33940260, 34096428, 34437964, 34635375, 34651575, 34791300, 34812414, 36128745, 36169920, 36205785, 36457960, 36835740, 37045435, 37056492, 37155915, 37274980, 37476801, 37699200, 38142819, 38629458, 38779497, 38954560, 39528247, 39620574, 39748500, 39854290, 40495950, 41034924, 41075550, 41294088, 41346760, 42595780, 42789456, 43695981, 44351793, 44699166, 45841950, 46853500, 46897452, 47589300, 47589768, 47851848, 49195894, 49198752, 49289760, 49698054, 49711662, 49786555, 50488996, 51590700, 51760962, 51868975, 51882930, 51899526, 51965914, 52173994, 52769574, 53716923, 53826106, 55294798, 56129076, 57201408, 59691037, 59771065, 61087950, 61305678, 62375800, 63962460, 68776960, 69174175, 69271200, 70978995, 71977405, 71983912, 72891364, 73895940, 75188592, 75698428, 75869640, 75990964, 76903848, 77329939, 79128657, 79680960, 80297127, 81290835, 84091945, 84372966, 86591974, 89901900.