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Chen prime  and  Proth n.

First numbers that belong to both sets:

3, 5, 13, 17, 41, 113, 257, 353, 449, 577, 641, 769, 1217, 1409, 1601, 3137, 3329, 3457, 4481, 7937, 9857, 10369, 11777, 12161, 13313, 13441, 14081, 16001, 17921, 23041, 23297, 25601, 30977, 32257, 37889, 39937, 40193, 41729, 43777, 45569, 46337, 49409, 51713, 57089, 58369, 60161, 65537, 76801, 83969, 96769, 114689, 119297, 119809, 133121, 136193, 153089, 155137, 159233, 163841, 168449, 176129, 183809, 184321, 211457, 211969, 226817, 232961, 242689, 249857, 260609, 285697, 286721, 326657, 329729, 345089, 414721, 428033, 455681, 471041, 495617, 498689, 514049, 557057, 572417, 649217, 658433, 667649, 685057, 721921, 765953, 772097, 778241, 793601, 808961, 836609, 838657, 921601, 928769, 930817, 974849, 979969, 995329, 1017857, 1054721, 1067009, 1073153, 1079297, 1097729, 1146881, 1239041, 1253377, 1288193, 1312769, 1355777, 1374209, 1417217, 1423361, 1503233, 1546241, 1589249, 1662977, 1669121, 1732609, 1785857, 1841153, 1847297, 1964033, 2021377, 2119681, 2297857, 2314241, 2369537, 2387969, 2437121, 2492417, 2572289, 2574337, 2664449, 2707457, 2775041, 2787329, 2836481, 2922497, 3002369, 3053569, 3082241, 3115009, 3168257, 3174401, 3219457, 3237889, 3266561, 3280897, 3291137, 3373057, 3383297, 3391489, 3414017, 3420161, 3573761, 3588097, 3604481, 3684353, 3690497, 3721217, 3782657, 3819521, 3942401, 3956737, 3985409, 4003841, 4046849, 4169729, 4304897, 4366337, 4464641, 4476929, 4550657, 4759553, 4771841, 4907009, 5140481, 5246977, 5287937, 5308417, 5337089, 5398529, 5431297, 5656577, 5677057, 5726209, 5767169, 5779457, 5804033, 6156289, 6234113, 6307841, 6320129, 6393857, 6455297, 6578177, 6737921, 6750209, 6873089, 6885377, 6942721, 6946817, 7090177, 7168001, 7438337, 7475201, 7548929, 7630849, 7659521, 7745537, 7806977, 7925761, 7979009, 8040449, 8114177, 8122369, 8257537, 8286209, 8519681, 8753153, 8814593, 8851457, 9011201, 9023489, 9035777, 9220097, 9392129, 9441281, 9453569, 9502721, 9711617, 9760769, 9781249, 10067969, 10362881, 10436609, 10534913, 10559489, 10571777, 10579969, 10629121, 10838017, 10989569, 11059201, 11186177, 11309057, 11345921, 11358209, 11468801, 11517953, 11591681, 11677697, 11759617, 12021761, 12046337, 12206081, 12230657, 12361729, 12390401, 12451841, 12587009, 12771329, 12820481, 12902401, 12906497, 13004801, 13029377, 13152257, 13283329, 13496321, 13541377, 13570049, 13631489, 13754369, 13877249.

Some larger examples :