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strong prime  and  truncatable prime

First numbers that belong to both sets:

17, 29, 37, 59, 67, 71, 79, 97, 137, 197, 223, 239, 311, 347, 367, 379, 397, 599, 613, 617, 673, 719, 739, 853, 937, 967, 1523, 1823, 1997, 2137, 2333, 2339, 2347, 2467, 2617, 2647, 2683, 2797, 2953, 3119, 3167, 3467, 3613, 3793, 4283, 4337, 4547, 4673, 4967, 5167, 5347, 5647, 5683, 6113, 6197, 6337, 6353, 6547, 6653, 6673, 6823, 6947, 6967, 6997, 7283, 7331, 7393, 7547, 8167, 8353, 8443, 9173, 9337, 9547, 9613, 9643, 9883, 9967, 12953, 13613, 15647, 16547, 16823, 23167, 23399, 23993, 24547, 24967, 26317, 26947, 27673, 27823, 27883, 29399, 31379, 32467, 32647, 32797, 33347, 33613, 33617, 36373, 36997, 37337, 37397, 37547, 37643, 38167, 38317, 39397, 39883, 42953, 43313, 43853, 48647, 49547, 51283, 56113, 56197, 56983, 57283, 59467, 59743, 61223, 61283, 62137, 62347, 62383, 62467, 62617, 62683, 63347, 63853, 64373, 65167, 65647, 66337, 66373, 66947, 67523, 67883, 68443, 69337, 71933, 72467, 72647, 72797, 73547, 73673, 73939, 75167, 75347, 75653, 76367, 78467, 79397, 79967, 81223, 83617, 86197, 87853, 91283, 91367, 91997, 92347, 93967, 94397, 96997, 97283, 97547, 97673, 98317, 98443, 98467, 99137, 99173, 99397, 99643, 121283, 121523, 124337, 136373, 139883, 184967, 187547, 195443, 215443, 231223, 233617, 234673, 236653, 237547, 242467, 243613, 261223, 264283, 266947, 273613, 279397, 279967, 291367, 293999, 297523, 299137, 313613, 326113, 326947, 327823, 332467, 336353, 337853, 338167, 342467, 348353, 356113, 356197, 362137, 362347, 363313, 364373, 364937, 368443, 372797, 373379, 373613, 373823, 375743, 379397, 384673, 387853, 391283, 391367, 392347, 392383, 392467, 392647, 395443, 397283, 397547, 397673, 398467, 399173, 399643, 424547, 429137, 432797, 439883, 453617, 454673, 459467, 462467, 463313, 463823, 465167, 481373, 493967, 496997, 498467, 516673, 534283, 536353, 536947, 542683, 543853, 549547, 566173, 566653, 573673, 578167, 578467, 593933, 594397, 613967, 621997, 626113, 626317, 626947, 629137, 631223, 633613.

Some larger examples :