Search a number
congruent n.  and  prime n.

First numbers that belong to both sets:

5, 7, 13, 23, 29, 31, 37, 41, 47, 53, 61, 71, 79, 101, 103, 109, 127, 137, 149, 151, 157, 167, 173, 181, 191, 197, 199, 223, 229, 239, 257, 263, 269, 271, 277, 293, 311, 313, 317, 349, 353, 359, 367, 373, 383, 389, 397, 421, 431, 439, 457, 461, 463, 479, 487, 503, 509, 541, 557, 599, 607, 613, 631, 647, 653, 661, 677, 701, 709, 719, 727, 733, 743, 751, 757, 761, 773, 797, 821, 823, 829, 839, 853, 863, 877, 887, 911, 919, 941, 967, 983, 991, 997, 1013, 1021, 1031, 1039, 1061, 1063, 1069, 1087, 1093, 1103, 1109, 1117, 1151, 1181, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1277, 1279, 1301, 1303, 1319, 1321, 1327, 1367, 1373, 1381, 1399, 1423, 1429, 1439, 1447, 1453, 1471, 1487, 1493, 1511, 1543, 1549, 1559, 1567, 1583, 1597, 1607, 1613, 1621, 1637, 1663, 1669, 1693, 1709, 1733, 1741, 1759, 1783, 1789, 1823, 1831, 1847, 1861, 1871, 1877, 1879, 1901, 1933, 1949, 1951, 1973, 1997, 1999, 2029, 2039, 2053, 2063, 2069, 2087, 2111, 2113, 2141, 2143, 2207, 2213, 2221, 2237, 2239, 2269, 2273, 2287, 2293, 2309, 2311, 2333, 2341, 2351, 2357, 2381, 2383, 2389, 2399, 2423, 2437, 2447, 2477, 2503, 2543, 2549, 2551, 2557, 2591, 2621, 2647, 2663, 2671, 2677, 2687, 2693, 2711, 2719, 2741, 2749, 2767, 2777, 2789, 2791, 2797, 2833, 2837, 2861, 2879, 2887, 2903, 2909, 2917, 2927, 2953, 2957, 2999, 3001, 3023, 3037, 3061, 3079, 3109, 3119, 3167, 3181, 3191, 3221, 3229, 3253, 3271, 3301, 3319, 3343, 3359, 3373, 3389, 3391, 3407, 3413, 3433, 3461, 3463, 3469, 3511, 3517, 3527, 3533, 3541, 3557, 3559, 3581, 3583, 3593, 3607, 3613, 3623, 3631, 3637, 3671, 3677, 3701.

Some larger examples :