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good prime  and  Honaker prime

First numbers that belong to both sets:

3433, 4903, 6563, 6653, 7411, 7523, 9103, 17317, 22613, 23531, 24841, 36433, 36523, 40427, 41131, 41141, 41941, 47293, 47491, 48463, 48473, 51131, 53591, 60601, 61253, 77237, 79133, 79273, 84313, 92347, 103979, 114451, 132607, 136177, 136207, 143443, 145451, 157013, 159403, 162493, 185519, 206909, 207923, 216551, 244291, 251051, 253243, 266003, 300137, 300647, 311677, 317257, 327193, 334289, 360821, 362851, 371057, 426637, 448627, 448801, 462307, 492403, 503707, 512419, 516157, 540167, 541129, 541217, 545527, 556177, 562181, 569711, 580607, 592057, 606721, 606731, 608357, 631121, 631151, 631453, 644051, 652237, 658111, 671903, 678401, 718337, 730447, 730747, 730777, 745529, 783119, 786803, 792023, 808343, 822551, 846341, 846661, 853667, 863479, 863633, 875183, 904019, 904067, 916831, 920729, 949931, 961087, 1033289, 1040747, 1040777, 1101299, 1104097, 1146263, 1155607, 1160807, 1160903, 1174423, 1178123, 1236419, 1236467, 1236953, 1238371, 1238381, 1242757, 1245509, 1253717, 1256659, 1298981, 1354931, 1422409, 1422583, 1422593, 1423319, 1424347, 1425427, 1502923, 1532543, 1533083, 1601423, 1616401, 1642243, 1652237, 1665023, 1667131, 1690009, 1695319, 1726139, 1820237, 1839347, 1841069, 1841891, 1851253, 1853177, 1925017, 1990103, 1990123, 1990133, 2032109, 2103553, 2135083, 2135641, 2139811, 2141669, 2154487, 2156269, 2202791, 2206327, 2224931, 2226149, 2226373, 2253037, 2317493, 2332373, 2357617, 2378423, 2433649, 2433967, 2439881, 2443729, 2518067, 2522593, 2547581, 2552449, 2559013, 2559041, 2573803, 2574167, 2574401, 2610077, 2630317, 2645051, 2809181, 2880149, 2995301, 3036427, 3037147, 3100807, 3102259, 3102269, 3138521, 3147563, 3149339, 3151373, 3162277, 3162487, 3164801, 3196163, 3255127, 3274031, 3303319, 3323833, 3384551, 3401591, 3401707, 3527941, 3593311, 3593321, 3606437, 3707287, 3711017, 3712063, 3712073, 3763423, 3776411, 3809123, 3809461, 3814309, 3873313, 3873323, 3921941, 3966503, 3991607, 4000489, 4005733, 4005943, 4021889, 4034449, 4034747, 4138241, 4146907, 4147873, 4147921, 4155409, 4155467, 4178327, 4178483, 4249391, 4249753, 4298023, 4402157, 4408093, 4409737, 4525091, 4526411, 4543207, 4553209, 4590181, 4606363, 4714439, 4800619, 4801603, 4831493, 4831531, 4835461, 4835471, 4835521, 4863553, 4863611, 4944307, 5065531, 5107643, 5107691, 5118821, 5119811, 5193037, 5193163, 5237251, 5283961, 5285129, 5287141.

Some larger examples :