First numbers that belong to both sets:
703,
2821,
2981,
3367,
4141,
5461,
6533,
6541,
7471,
8149,
8911,
10001,
11111,
13981,
14701,
14911,
15841,
22321,
24013,
24661,
27613,
29341,
34133,
38503,
41041,
45527,
46657,
50851,
57181,
63973,
65311,
66991,
67861,
68101,
83119,
101101,
102173,
118301,
118957,
122221,
130351,
131821,
134821,
134863,
137149,
138481,
139231,
145181,
152551,
162401,
164761,
172081,
188191,
188269,
188461,
188501,
201917,
216001,
225589,
234421,
248677,
250717,
251251,
274231,
281821,
286903,
287749,
294409,
314821,
334153,
341503,
364277,
390313,
391141,
410041,
420343,
489997,
491063,
492101,
497503,
497927,
509971,
512461,
522349,
585631,
595231,
597871,
632641,
634351,
679861,
710533,
741751,
748657,
765703,
847693,
853381,
873181,
880237,
886033,
909709,
981317,
997981,
1033669,
1039441,
1111111,
1128871,
1141141,
1146401,
1152271,
1163801,
1167607,
1168513,
1169101,
1171261,
1193221,
1251949,
1268551,
1272271,
1294411,
1308853,
1362061,
1398101,
1419607,
1446241,
1446661,
1462441,
1463749,
1492663,
1498981,
1531711,
1543381,
1551941,
1576381,
1583821,
1590751,
1615681,
1703221,
1705621,
1711381,
1756351,
1803413,
1826209,
1887271,
1892143,
1926761,
1942957,
1943341,
1945423,
1953671,
1991821,
2030341,
2085301,
2100901,
2146957,
2161501,
2165801,
2171197,
2194973,
2205967,
2337301,
2358533,
2386141,
2463661,
2503501,
2508013,
2525909,
2539183,
2553061,
2563903,
2585701,
2603381,
2630071,
2699431,
2719981,
2795519,
2824061,
2879317,
2887837,
2899351,
2916511,
2949991,
2976487,
2987167,
3057601,
3146221,
3186821,
3209053,
3247453,
3369421,
3387781,
3400013,
3429889,
3471071,
3506221,
3536821,
3581761,
3593551,
3677741,
3740737,
3781141,
3817681,
3862207,
3985921,
4010401,
4014241,
4064677,
4077151,
4099439,
4119301,
4209661,
4234021,
4255903,
4260301,
4326301,
4363261,
4363661,
4373461,
4415581,
4469471,
4469551,
4499701,
4504501,
4543621,
4630141,
4762381,
4806061,
4863127,
4917781,
5031181,
5122133,
5160013,
5197837,
5203471,
5292631,
5308181,
5474657,
5478913,
5481451,
5495023,
5502061,
5718721,
5780941,
5804821,
5824711,
5887189,
5892511,
5934391,
5943301,
5950501,
5956741,
6096181,
6189121,
6298513,
6457951,
6469789,
6539821,
6544561,
6724861,
6733693,
6822541,
6868261,
6906901,
6934951,
6969511,
6997981,
7071181,
7262413,
7406311,
7428421,
7434541,
7455481,
7532713,
7624501,
7652101,
7678501,
7683397,
7686401,
7686647,
7765759,
7968511.
Some larger examples :
8719309,
8719921,
8769949,
8835301,
8889791,
8927101,
8948701,
9004801,
9069229,
9336961,
9411911,
9417331,
9493903,
9494101,
9515143,
9567673,
9585541,
9756839,
9776701,
9863461.