1. Left truncatable prime
1.1. Largest left-truncatable prime in base n written in base 10 for 3<=n<=36: (since no such primes exist in base 2)
23, 4091, 7817, 4836525320399, 817337, 14005650767869, 1676456897, 357686312646216567629137, 2276005673, 13092430647736190817303130065827539, 812751503, 615419590422100474355767356763, 34068645705927662447286191, 1088303707153521644968345559987, 13563641583101, 571933398724668544269594979167602382822769202133808087, 546207129080421139, 1073289911449776273800623217566610940096241078373, 391461911766647707547123429659688417, 33389741556593821170176571348673618833349516314271, 116516557991412919458949, 10594160686143126162708955915379656211582267119948391137176997290182218433, 8211352191239976819943978913, 12399758424125504545829668298375903748028704243943878467, 10681632250257028944950166363832301357693, 720639908748666454129676051084863753107043032053999738835994276213, 4300289072819254369986567661, ?, 645157007060845985903112107793191, 1131569863270120248974817136287838489359936416046975582122661310411, 924039815258046855588818237912726885772934968646554431, 982498935397824993800810311994840611581693708091339679644860318739434026149, 448739985000415097566502155600731235704288431019152509, ? (A103443)
1.2. Largest left-truncatable prime in base n written in base n for 3<=n<=36: (since no such primes exist in base 2)
212, 333323, 222232, 14141511414451435, 6642623, 313636165537775, 4284484465, 357686312646216567629137, A68822827, 471A34A164259BA16B324AB8A32B7817, CC4C8C65, D967CCD63388522619883A7D23, 6C6C2CE2CEEEA4826E642B, DBC7FBA24FE6AEC462ABF63B3, 6C66CC4CC83, AF93E41A586HE75A7HHAAB7HE12FG79992GA7741B3D, CIEG86GCEA2C6H, FC777G3CG1FIDI9I31IE5FFB379C7A3F6EFID, G8AGG2GCA8CAK4K68GEA4G2K22H, FFHALC8JFB9JKA2AH9FAB4I9L5I9L3GF8D5L5, IMMGM6C6IMCI66A4H, HMJEJFA3A71DID9MFMNFE3D3KJHA61KH92IFCA3LB8GF444FBB7AH, ME6OM6OECGCC24C6EG6D, L2K853AC9IC628859L93F7FLAM7L25EN3C3PC27, O2AKK6EKG844KAIA4MACK6C2ECAB, 5C9126C3PN6IRP5FPBMKA5LGBMO387R5IJLO54OFBFJL85, KCG66AGSCKEIASMCKKJ, ?, UUAUIKUC4UI6OCECI642SD, LFLHKUDGSP39SAAPAD9I9OLIOUOH6GV68OR8UMJ6LRUB, 6ISWQOIMIWC8OKQAIMKUQ24KO86WK2ASCEC5, U9WSWU4T672RCMFESU6B6FG99UNABPFOU2LIIUGTX1KABJBPV, E8KUSUKKQEQWEWCMIEOY46Q8888QOSAAYOJ, ?
1.3. Length of largest left-truncatable prime in base n for 3<=n<=36: (since no such primes exist in base 2)
3, 6, 6, 17, 7, 15, 10, 24, 9, 32, 8, 26, 22, 25, 11, 43, 14, 37, 27, 37, 17, 53, 20, 39, 28, 46, 19, (about 82 in theory), 22, 44, 36, 49, 35, (about 76 in theory) (A103463)
1.4. Number of left-truncatable primes in base n for 2<=n<=36:
0, 3, 16, 15, 454, 22, 446, 108, 4260, 75, 170053, 100, 34393, 9357, 27982, 362, 14979714, 685, 3062899, 59131, 1599447, 1372, 1052029701, 10484, 7028048, 98336, 69058060, 3926, (about 16844070429770 in theory), 11314, 35007483, 2527304, 240423316, 607905, (about 1631331033450 in theory) (A076623)
2. Right truncatable prime
2.1. Largest right-truncatable prime in base n written in base 10 for 3<=n<=36: (since no such primes exist in base 2)
71, 191, 2437, 108863, 6841, 4497359, 1355840309, 73939133, 6774006887, 18704078369, 122311273757, 6525460043032393259, 927920056668659, 16778492037124607, 4928397730238375565449, 5228233855704101657, 3013357583408354653, 1437849529085279949589, 101721177350595997080671, 185720479816277907890970001, 158208158913013692383, 192747244030905257036482742599289, 11360039924980123824119977, 522764314648992960422987767, 106521223483392113109841556843, 467437774672035454997088263971, 18980691336146397055451904000521, 206971354022501468249535515240921, 403878995374635723531460715056361, 9813093725765026702961210138094949, 10174889780995609522983172669668593, 18085876810004448001794542893991790487, 9520817609816167868579578513867491007, 8723727825272063982605771015871962141 (A023107)
2.2. Largest right-truncatable prime in base n written in base n for 3<=n<=36: (since no such primes exist in base 2)
2122, 2333, 34222, 2155555, 25642, 21117717, 3444224222, 73939133, 29668286AA, 375BB5B515, B6C2CA8A8A, 2DD35B9D399395B3D, 72424E42EEE8E, 3B9BF319BD51FF, 5G4CEE8EC688CAC86G, DH17HB7BBD75BDB, 3EC8GI8GICIEG8C, 23HBH9D19HH9JDDJ9, 3824A4GGA4AG82KKA8, 5H975FFLLJF3HL3F33F3, DEK6ICCE8EE2K26, 3B5J511H5NJNN55B7JDBNN7H, JCMIIIEIIOIC4EIGO2, HJ1FHN97JF9P7PFFJ19, 2DMMKQEMAM4884QMAEAG2, 5953R9JHJ5PFF3R3H3D9N, 3K6QOO6682O4AG4GG6Q82C, JNHJ77DDNT7THDD177HD7B, JC642UIS2S8GOQUSKMII2A, 7HT59VF3PDRRJ7PD3371RB5, 3WEK8QAGQW8GW4E4KWGEAA2, 35X5FPF5R7XBXD9LRB1BRXXVT, T6CGG4G68I4MC26GCOYYCWCC, DZJZJPDDP7J55ZNPPZ71PD7H
2.3. Length of largest right-truncatable prime in base n for 3<=n<=36: (since no such primes exist in base 2)
4, 4, 5, 7, 5, 8, 10, 8, 10, 10, 10, 17, 13, 14, 18, 15, 15, 17, 18, 20, 15, 24, 18, 19, 21, 21, 22, 22, 22, 23, 23, 25, 24, 24 (A103483)
2.4. Number of right-truncatable primes in base n for 2<=n<=36:
0, 4, 7, 14, 36, 19, 68, 68, 83, 89, 179, 176, 439, 373, 414, 473, 839, 1010, 1577, 2271, 2848, 1762, 3376, 5913, 6795, 6352, 10319, 5866, 14639, 13303, 19439, 29982, 38956, 39323, 58857 (A076586)
3. Two-sided prime (both left truncatable and right truncatable)
3.1. Largest two-sided prime in base n written in base 10 for 3<=n<=36: (since no such primes exist in base 2)
23, 11, 67, 839, 37, 1867, 173, 739397, 79, 105691, 379, 37573, 647, 3389, 631, 202715129, 211, 155863, 1283, 787817, 439, 109893629, 577, 4195880189, 1811, 14474071, 379, 21335388527, 2203, 1043557, 2939, 42741029, 2767, 50764713107 (A323137)
3.2. Largest two-sided prime in base n written in base n for 3<=n<=36: (since no such primes exist in base 2)
212, 23, 232, 3515, 52, 3513, 212, 739397, 72, 511B7, 232, D99B, 2D2, D3D, 232, 5H511HB, B2, J9D3, 2J2, 37LFJ, J2, DJ5BD5, N2, DF3LL97, 2D2, NF9N3, D2, T7TTH7H, 292, VR35, 2N2, VXF73, 292, NBJZZBN
3.3. Length of largest two-sided prime in base n for 3<=n<=36: (since no such primes exist in base 2)
3, 2, 3, 4, 2, 4, 3, 6, 2, 5, 3, 4, 3, 3, 3, 7, 2, 4, 3, 5, 2, 6, 2, 7, 3, 5, 2, 7, 3, 4, 3, 5, 3, 7
3.4. Number of two-sided primes in base n for 3<=n<=36:
0, 2, 3, 5, 9, 7, 22, 8, 15, 6, 35, 11, 37, 17, 22, 12, 69, 12, 68, 18, 44, 13, 145, 16, 47, 20, 77, 13, 291, 15, 89, 27, 74, 20, 241 (A323390)
4. Minimal prime
4.1. Largest minimal prime in base n written in base 10 for 2<=n<=36:
3, 13, 5, 3121, 5209, 2801, 76695841, 811, 66600049, 29156193474041220857161146715104735751776055777, 388177921, 13^32020*8+183, 105424857819287798806418819113233738918727566030978473259776662287591943095417282958456246916612161, 436635814641280043127962407363407208906111673434962498607709751248805460292422544779495998033626489944124062146459306989397233, 16^3544*9+145, >=(73*17^111333-9)/16, 249069897374447078426903207266791381270529, >=(904*19^110984-1)/3, (20^449*16-2809)/19, >=(51*21^479149-1243)/4, 22^763*20+7041, (23^800873*106-7)/11, 973767003942195520947294504280890002680537875404412883659428819153939518991719953852457999342229586282557076411687300474817686178175693329, >=(37*25^136966+63)/4, >=(22*26^8773+53)/25, >=10*27^109005+697, >=(6092*28^94536-143)/9, >=24*29^174239+13361, 30^1023*12+1, >=(5727*31^29787-7)/10, >=(898*32^9749-309)/31, >=(21*33^9961+7723)/32, 1048*34^9375+27, (13456*35^9597-9)/17, (5*36^81995+821)/7 (A326609)
4.2. Largest minimal prime in base n written in base n for 2<=n<=36:
11, 111, 11, 44441, 40041, 11111, 444444441, 1101, 66600049, 444444444444444444444444444444444444444444441, AA000001, 8(0^32017)111, 40000000000000000000000000000000000000000000000000000000000000000000000000000000000049, 96666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666608, 9(0^3542)91, >=4(9^111333), GG0000000000000000000000000000001, >=FG(6^110984), (G^447)99, >=C(F^479147)0K, K(0^760)EC1, 9(E^800873), M666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661, >=9(6^136965)M, >=(M^8772)P, >=A(0^109003)PM, >=O4(O^94535)9, >=O(0^174236)FPL, C(0^1022)1, >=IE(L^29787), >=S(U^9748)L, >=(L^9959)SW, >=US(0^9374)R, >=ML(I^9597), >=(P^81993)SZ
4.3. Length of largest minimal prime in base n for 2<=n<=36:
2, 3, 2, 5, 5, 5, 9, 4, 8, 45, 8, 32021, 86, 107, 3545, >=111334, 33, >=110986, 449, >=479150, 764, 800874, 100, >=136967, >=8773, >=109006, >=94538, >=174240, 1024, >=29789, >=9750, >=9961, >=9377, >=9599, >=81995 (A330049)
4.4. Number of minimal primes in base n for 2<=n<=36:
2, 3, 3, 8, 7, 9, 15, 12, 26, 152, 17, 228, 240, 100, 483, 1279~1280, 50, 3462~3463, 651, 2600~2601, 1242, 6021, 306, 17597~17609, 5662~5664, 17210~17215, 5783~5784, 57283~57297, 220, 79189~79203, 45205~45283, 57676~57709, 56457~56490, 182378~182393, 6296~6297 (A330048)
5. Weakly prime
5.1. Smallest weakly prime in base n written in base 10 for 2<=n<=36:
127, 2, 373, 83, 28151, 223, 6211, 2789, 294001, 3347, 20837899, 4751, 6588721, 484439, 862789, 10513, 2078920243, 10909, 169402249, 2823167, 267895961, 68543, 1016960933671, 181141, 121660507, 6139219, 11646280537, 488651, >2*10^12, 356479, ?, 399946711, ?, 22549349, ? (A186995)
5.2. Smallest weakly prime in base n written in base n for 2<=n<=36:
1111111, 2, 11311, 313, 334155, 436, 14103, 3738, 294001, 2573, 6B8AB77, 2216, C371CD, 9880E, D2A45, 2267, 3723DE91, 1B43, 2CIF5C9, EAHFB, 27LD613, 5ED3, 95HCJA8C7, BEKG, A65P47, BEOBD, O4JHPIH, K111, >31DEFO26K, BTTA, ?, A783HA, ?, F0WM4, ?
5.3. Length of smallest weakly prime in base n written in base n for 2<=n<=36:
7, 1, 5, 3, 6, 3, 5, 4, 6, 4, 7, 4, 6, 5, 5, 4, 8, 4, 7, 5, 7, 4, 9, 4, 6, 5, 7, 4, >=9, 4, ?, 6, ?, 5, ?
6. Permutable prime
6.1. Largest permutable prime in base n (repunit primes excluded) written in base 10 for 3<=n<=36: (since no such primes exist for base 2) (conjectured)
7, 53, 3121, 211, 1999, 3803, 6469, 991, 161047, 19793, 16477, 24907, 683437, 3547, 67853, 80273, 94109, 72421, 148639, 182537, 228953, 9967, 358069, 17467, 99929, 21943, 369319, 26981, 23580569, 1048571, 1037657, 1012369, 1271117, 1367687 (A317689)
6.2. Largest permutable prime in base n (repunit primes excluded) written in base n for 3<=n<=36: (since no such primes exist for base 2) (conjectured)
21, 311, 44441, 551, 5554, 7333, 8777, 991, AAAA7, B555, 7666, 9111, D7777, DDB, DDD6, DDDB, DDD2, 9111, G111, H333, IIIB, H77, MMMJ, PLL, 5222, RRJ, F444, TTB, PGGGG, VVVR, SSS5, PPPJ, TMMM, TBBB
6.3. Length of largest permutable prime in base n (repunit primes excluded) for 3<=n<=36: (since no such primes exist for base 2) (conjectured)
2, 3, 5, 3, 4, 4, 4, 3, 5, 4, 4, 4, 5, 3, 4, 4, 4, 4, 4, 4, 4, 3, 4, 3, 4, 3, 4, 3, 5, 4, 4, 4, 4, 4
6.4. Number of permutable primes in base n (repunit primes excluded) for 2<=n<=36: (conjectured)
0, 3, 7, 13, 8, 27, 16, 30, 21, 69, 21, 70, 31, 50, 38, 46, 42, 93, 50, 83, 58, 106, 37, 139, 69, 89, 70, 176, 56, 187, 80, 111, 147, 201, 102
7. Circular prime (data only available for bases <=12)
7.1. Largest circular prime in base n (repunit primes excluded) written in base 10 for 3<=n<=12: (since no such primes exist for base 2) (conjectured)
7, 1013, 3121, 211, 13143449029, 16244441, 4717103, 999331, 378470237117827, 2894561 (A293142)
7.2. Largest circular prime in base n (repunit primes excluded) written in base n for 3<=n<=12: (since no such primes exist for base 2) (conjectured)
21, 33311, 44441, 551, 643464321244, 75757331, 8778575, 999331, AA657365177398, B77115
7.3. Length of largest circular prime in base n (repunit primes excluded) for 3<=n<=12: (since no such primes exist for base 2) (conjectured)
2, 5, 5, 3, 12, 8, 7, 6, 14, 6
7.4. Number of circular primes in base n (repunit primes excluded) for 2<=n<=12: (conjectured)
0, 3, 10, 24, 5, 141, 42, 50, 54, ?, 37
8. Repunit prime
8.1. Smallest repunit prime in base n written in base 10 for 2<=n<=36: (0 if no such primes exist)
3, 13, 5, 31, 7, 2801, 73, 0, 11, 50544702849929377, 13, 30941, 211, 241, 17, 307, 19, 109912203092239643840221, 421, 463, 23, 292561, 601, 0, 321272407, 757, 29, 732541, 31, 917087137, 0, 1123, 2458736461986831391, (35^313-1)/34, 37 (A084738)
8.2. Smallest repunit prime in base n written in base n for 2<=n<=36: (0 if no such primes exist)
11, 111, 11, 111, 11, 11111, 111, 0, 11, 11111111111111111, 11, 11111, 111, 111, 11, 111, 11, 1111111111111111111, 111, 111, 11, 11111, 111, 0, 1111111, 111, 11, 11111, 11, 1111111, 0, 111, 1111111111111, (1^313), 11
8.3. Length of smallest repunit prime in base n written in base n for 2<=n<=36: (0 if no such primes exist)
2, 3, 2, 3, 2, 5, 3, 0, 2, 17, 2, 5, 3, 3, 2, 3, 2, 19, 3, 3, 2, 5, 3, 0, 7, 3, 2, 5, 2, 7, 0, 3, 13, 313, 2 (A084740)