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Cunningham n.  and  weak prime

First numbers that belong to both sets:

3, 7, 31, 401, 577, 677, 1601, 2917, 3137, 8101, 8191, 12101, 15377, 24337, 42437, 50177, 55697, 57601, 62501, 69697, 80657, 93637, 131071, 147457, 148997, 190097, 246017, 287297, 309137, 324901, 404497, 414737, 417317, 484417, 524287, 562501, 583697, 608401, 665857, 933157, 1008017, 1123601, 1166401, 1223237, 1263377, 1299601, 1308737, 1313317, 1378277, 1401857, 1552517, 1623077, 1628177, 1664101, 1674437, 1731857, 1742401, 1822501, 1893377, 1976837, 2232037, 2402501, 2464901, 2611457, 2735717, 2768897, 2802277, 2835857, 3013697, 3083537, 3218437, 3326977, 3459601, 3496901, 3865157, 3880901, 3896677, 3960101, 4104677, 4137157, 4202501, 4218917, 4301477, 4477457, 4494401, 4519877, 4639717, 4884101, 5134757, 5225797, 5354597, 5541317, 5664401, 6031937, 6330257, 6502501, 6728837, 6885377, 7001317, 7043717, 7096897, 7203857, 7290001, 7322437, 7485697, 7584517, 7706177, 8202497, 8271377, 8317457, 8549777, 9096257, 9156677, 9821957, 9834497, 10074277, 10265617, 10329797, 10719077, 10824101, 11115557, 11155601, 11222501, 11289601, 11874917, 12180101, 13278737, 13586597, 13808657, 14092517, 14107537, 14167697, 14258177, 14394437, 14440001, 15085457, 15210001, 15288101, 15570917, 15729157, 15872257, 16048037, 16192577, 16370117, 16451137, 16646401, 16695397, 16924997, 17007377, 17272337, 17438977, 17505857, 17859077, 18198757, 18576101, 18800897, 19044497, 19061957, 19096901, 19131877, 19749137, 20124197, 20214017, 20340101, 20520901, 20557157, 20611601, 20738917, 21068101, 21196817, 21215237, 21566737, 21771557, 22090001, 22240657, 22410757, 22600517, 22848401, 22982437, 23951237, 24443137, 24542117, 24561937, 25040017, 25300901, 25441937, 25542917, 25806401, 26275877, 26832401, 27311077, 27415697, 28558337, 28836901, 29203217, 29376401, 29419777, 29877157, 29964677, 29986577, 30096197, 30316037, 30647297, 30802501, 30958097, 31069477, 31181057, 31248101, 32080897, 32490001, 32604101, 33131537, 33802597, 34222501, 34292737, 34409957, 34527377, 34574401, 35331137, 35521601, 35640901, 36360901, 36554117, 37161217, 37454401, 37576901, 38142977, 38638657, 39765637, 40322501, 40449601, 40525957, 41396357, 43243777, 43428101, 43744997, 44036497, 45077797, 45751697, 45914177, 46022657, 46049797, 46321637, 46977317, 47141957, 48385937, 48860101, 48944017, 49224257, 49702501, 49928357, 50836901, 51322897, 52070657, 52417601, 52707601, 53348417, 53670277, 54228497, 54523457, 54908101, 54967397, 55591937, 55860677, 56490257, 56610577, 59598401, 59814757, 60124517, 60372901, 60435077, 60528401, 61152401, 61402897, 61842497, 62568101, 63138917, 64224197, 66814277, 67141637.

Some larger examples :