Search a number
modest n.  and  weak prime

First numbers that belong to both sets:

13, 19, 23, 89, 103, 109, 199, 233, 409, 433, 509, 709, 811, 911, 1033, 1433, 1499, 1699, 1933, 1999, 2003, 2099, 2399, 2633, 2699, 3499, 4027, 4099, 4111, 5333, 5399, 6199, 7027, 7333, 8599, 8699, 10009, 10111, 10303, 10333, 10909, 13037, 13999, 16111, 17333, 19037, 19333, 20333, 22111, 25037, 25999, 28111, 32999, 33037, 35111, 35999, 36037, 38333, 40099, 49333, 49999, 50033, 50101, 50333, 55333, 56333, 56999, 58111, 61333, 64333, 70009, 70999, 71333, 71999, 79111, 79999, 80111, 85333, 85999, 90011, 92111, 94111, 95111, 98999, 100003, 100271, 103333, 104999, 109111, 121333, 130099, 133999, 136999, 137999, 139999, 140909, 143333, 155333, 160033, 170101, 172999, 175333, 176333, 178333, 182999, 184999, 188333, 200003, 200009, 200033, 200041, 200909, 209333, 210101, 212999, 220333, 236333, 239333, 242999, 247999, 266999, 268999, 269333, 272333, 277999, 280099, 280303, 286333, 287333, 290999, 295333, 298999, 299333, 301333, 301999, 308333, 310333, 313333, 317333, 320303, 322999, 325999, 328333, 329333, 329999, 331999, 338999, 353333, 356999, 361111, 379999, 390101, 400009, 400123, 409999, 415999, 430303, 430909, 430999, 436999, 440101, 448999, 455999, 460099, 464999, 470303, 470999, 473999, 478999, 484999, 496999, 497999, 500041, 500369, 506999, 510101, 511111, 517999, 521999, 529999, 530303, 533999, 535999, 541999, 542999, 550909, 556999, 563999, 571111, 580303, 584999, 587999, 599999, 608999, 611999, 613999, 616999, 620303, 638999, 652999, 667999, 668999, 670099, 670303, 671999, 688999, 691111, 694999, 697999, 702439, 704999, 720101, 721111, 725999, 730999, 731999, 733333, 740099, 740303, 742999, 745999, 764999, 769999, 770909, 781999, 787999, 790099, 799999, 800123, 800909, 803333, 820909, 821999, 839999, 850303, 854999, 868999, 880303, 880909, 884999, 886999, 890303, 893999, 901111, 904999, 907999, 910099, 910909, 911111, 913999, 941999, 956999, 970303, 970909, 970999, 971111, 973333, 974999, 1000003, 1000039, 1000333, 1000429, 1000777, 1002457, 1003003, 1008547, 1039999, 1100041, 1100909, 1133333, 1163333, 1171111, 1199999, 1229999, 1253333, 1270909, 1273333, 1343333, 1363333, 1370909.

Some larger examples :