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Cunningham n.  and  strong prime

First numbers that belong to both sets:

17, 37, 101, 127, 197, 1297, 4357, 5477, 7057, 8837, 14401, 15877, 16901, 17957, 21317, 22501, 25601, 28901, 32401, 41617, 44101, 52901, 65537, 67601, 72901, 78401, 90001, 106277, 115601, 122501, 156817, 160001, 164837, 184901, 193601, 197137, 215297, 217157, 220901, 224677, 240101, 295937, 331777, 341057, 352837, 401957, 454277, 462401, 470597, 476101, 490001, 495617, 509797, 512657, 547601, 614657, 682277, 739601, 746497, 792101, 820837, 828101, 846401, 864901, 876097, 894917, 902501, 921601, 972197, 1020101, 1073297, 1110917, 1136357, 1144901, 1196837, 1201217, 1322501, 1336337, 1382977, 1464101, 1547537, 1705637, 1726597, 1752977, 1795601, 1833317, 1865957, 1887877, 1943237, 2005057, 2016401, 2044901, 2056357, 2073601, 2119937, 2131601, 2262017, 2421137, 2446097, 2452357, 2483777, 2496401, 2515397, 2604997, 2689601, 2702737, 2755601, 2808977, 2890001, 2944657, 3118757, 3147077, 3182657, 3204101, 3297857, 3422501, 3519377, 3549457, 3587237, 3648101, 3686401, 3763601, 3857297, 3920401, 4024037, 4227137, 4260097, 4326401, 4343057, 4351397, 4384837, 4393217, 4435237, 4562497, 4726277, 4946177, 5107601, 5262437, 5308417, 5336101, 5382401, 5410277, 5428901, 5456897, 5569601, 5779217, 5788837, 5856401, 5904901, 6022117, 6051601, 6071297, 6100901, 6230017, 6421157, 6431297, 6604901, 6635777, 6760001, 6780817, 7107557, 7452901, 7540517, 7617601, 7650757, 7672901, 7728401, 7806437, 7862417, 7974977, 8031557, 8042897, 8122501, 8352101, 8386817, 8410001, 8503057, 8561477, 8608357, 8667137, 8761601, 8785297, 8844677, 8916197, 9278117, 9326917, 9572837, 9647237, 9672101, 9859601, 9960337, 9985601, 10137857, 10368401, 10497601, 10536517, 10588517, 10666757, 10758401, 10916417, 10929637, 11062277, 11262737, 11383877, 11492101, 11806097, 12068677, 12110401, 12362257, 12390401, 12460901, 12503297, 13322501, 13395601, 13468901, 13912901, 13942757, 14032517, 14243077, 14318657, 14364101, 14485637, 14638277, 14822501, 14976901, 15132101, 15163237, 15397777, 15952037, 16564901, 16974401, 17106497, 17139601, 17189317, 17255717, 17388901, 17422277, 17472401, 17690437, 18062501, 18147601, 18438437, 18490001, 18748901, 18835601, 19395217, 19855937, 20016677, 20286017, 20466577, 20848357, 21160001, 21288997, 21307457, 22127617, 22335077, 22429697, 22886657, 23001617, 23367557, 23522501, 23775377, 23872997, 24049217, 24108101, 24206401, 24364097, 24900101, 25140197, 25160257, 25563137, 25765777, 25867397, 26214401, 26563717, 26728901, 26790977, 26977637, 27040001, 27081617.

Some larger examples :