Search a number
modest n.  and  prime n.

First numbers that belong to both sets:

13, 19, 23, 29, 59, 79, 89, 103, 109, 199, 211, 233, 311, 409, 433, 499, 509, 599, 709, 733, 809, 811, 911, 1009, 1033, 1399, 1433, 1499, 1699, 1733, 1933, 1999, 2003, 2027, 2099, 2111, 2333, 2399, 2633, 2699, 2833, 2999, 3037, 3299, 3499, 4027, 4099, 4111, 4799, 4999, 5009, 5099, 5333, 5399, 6037, 6199, 6299, 6599, 6899, 7027, 7333, 7499, 7699, 8009, 8111, 8599, 8699, 8999, 9199, 10009, 10037, 10099, 10111, 10303, 10333, 10909, 11027, 12037, 13037, 13999, 16111, 16333, 17027, 17333, 19037, 19333, 20011, 20101, 20333, 22027, 22037, 22111, 23027, 23333, 25037, 25111, 25999, 26111, 28111, 29333, 30011, 31333, 32999, 33037, 35111, 35999, 36037, 38333, 40009, 40099, 40111, 41333, 41999, 44111, 47111, 49333, 49999, 50033, 50101, 50111, 50333, 50909, 52999, 55333, 56333, 56999, 58111, 59333, 59999, 60101, 61333, 64333, 65111, 68111, 70009, 70099, 70111, 70999, 71333, 71999, 73999, 76333, 77999, 79111, 79333, 79999, 80111, 80909, 85333, 85999, 86111, 90011, 92111, 92333, 94111, 94999, 95111, 98999, 100003, 100271, 100333, 100999, 101111, 101333, 101999, 103333, 104999, 107999, 109111, 110909, 121333, 130099, 130303, 131111, 133999, 134333, 134999, 136333, 136999, 137999, 139333, 139999, 140333, 140909, 143333, 143999, 149333, 154333, 155333, 157999, 160033, 161333, 161999, 164999, 170099, 170101, 172999, 175333, 176333, 178333, 179999, 182333, 182999, 184333, 184999, 188333, 188999, 190909, 191999, 199999, 200003, 200009, 200033, 200041, 200909, 202999, 203999, 208333, 209333, 210101, 211333, 212999, 217333, 220333, 221999, 223999, 230101, 230303, 230999, 232333, 236333, 239333, 239999, 240101, 241333, 242999, 244333, 247999, 253999, 260999, 265333, 266333, 266999, 268999, 269333, 271333, 272333, 272999, 274333, 275999, 277999, 280099, 280303, 280909, 286333, 286999, 287333, 289999, 290033, 290999, 293999, 295333, 298999, 299333, 301333, 301999, 302999, 305999, 308333, 308999, 310333, 311111, 313333, 317333, 320101, 320303, 322999, 323333, 325333, 325999.

Some larger examples :