First numbers that belong to both sets:
11,
17,
41,
71,
101,
127,
223,
227,
307,
311,
347,
727,
1277,
1423,
1427,
2203,
4001,
4201,
4211,
4217,
4441,
4447,
7411,
7477,
10007,
11047,
11777,
12227,
12373,
12377,
12473,
14243,
14321,
14401,
14407,
17317,
17377,
20707,
20717,
20743,
21377,
23003,
23741,
27407,
27427,
40423,
40427,
40471,
41011,
41141,
41177,
47041,
47111,
70001,
70111,
70117,
71143,
73277,
73303,
73327,
74017,
74047,
74143,
74707,
77417,
77471,
77477,
101107,
101111,
104471,
110477,
111427,
127207,
127217,
127241,
127247,
127447,
143401,
143443,
143477,
144241,
144247,
200771,
201401,
201473,
217111,
222773,
224027,
227011,
227147,
227371,
240701,
241303,
243073,
243401,
243421,
244121,
244217,
244243,
274777,
302747,
303271,
312007,
312023,
317321,
324011,
324427,
327247,
327401,
340027,
340777,
344171,
370373,
370411,
371027,
371227,
372707,
407177,
407203,
414017,
417007,
470077,
473141,
702101,
702127,
702173,
702311,
704003,
720743,
723043,
744371,
747277,
747377,
747401.