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Search a number
amenable n.  and  prime n.

First numbers that belong to both sets:

5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281, 293, 313, 317, 337, 349, 353, 373, 389, 397, 401, 409, 421, 433, 449, 457, 461, 509, 521, 541, 557, 569, 577, 593, 601, 613, 617, 641, 653, 661, 673, 677, 701, 709, 733, 757, 761, 769, 773, 797, 809, 821, 829, 853, 857, 877, 881, 929, 937, 941, 953, 977, 997, 1009, 1013, 1021, 1033, 1049, 1061, 1069, 1093, 1097, 1109, 1117, 1129, 1153, 1181, 1193, 1201, 1213, 1217, 1229, 1237, 1249, 1277, 1289, 1297, 1301, 1321, 1361, 1373, 1381, 1409, 1429, 1433, 1453, 1481, 1489, 1493, 1549, 1553, 1597, 1601, 1609, 1613, 1621, 1637, 1657, 1669, 1693, 1697, 1709, 1721, 1733, 1741, 1753, 1777, 1789, 1801, 1861, 1873, 1877, 1889, 1901, 1913, 1933, 1949, 1973, 1993, 1997, 2017, 2029, 2053, 2069, 2081, 2089, 2113, 2129, 2137, 2141, 2153, 2161, 2213, 2221, 2237, 2269, 2273, 2281, 2293, 2297, 2309, 2333, 2341, 2357, 2377, 2381, 2389, 2393, 2417, 2437, 2441, 2473, 2477, 2521, 2549, 2557, 2593, 2609, 2617, 2621, 2633, 2657, 2677, 2689, 2693, 2713, 2729, 2741, 2749, 2753, 2777, 2789, 2797, 2801, 2833, 2837, 2857, 2861, 2897, 2909, 2917, 2953, 2957, 2969, 3001, 3037, 3041, 3049, 3061, 3089, 3109, 3121, 3137, 3169, 3181, 3209, 3217, 3221, 3229, 3253, 3257, 3301, 3313, 3329, 3361, 3373, 3389, 3413, 3433, 3449, 3457, 3461, 3469, 3517, 3529, 3533, 3541, 3557, 3581, 3593, 3613, 3617, 3637, 3673, 3677, 3697, 3701, 3709, 3733, 3761, 3769, 3793, 3797, 3821, 3833, 3853, 3877, 3881, 3889, 3917, 3929, 3989, 4001, 4013, 4021, 4049, 4057, 4073, 4093, 4129, 4133, 4153, 4157.

Some larger examples :