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Old 2020-11-03, 09:06   #1
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Default Type of primes in various bases

1. Permutable prime

1.1. 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

1.2. 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

1.3. 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

1.4. Number of permutable primes in base n (repunit primes excluded) for 2<=n<=36: (conjectured)

2. Left-truncatable prime

2.1. Largest left-truncatable prime in base n written in base 10 for 3<=n<=36: (since no such primes exist for 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, ?

2.2. Largest left-truncatable prime in base n written in base n for 3<=n<=36: (since no such primes exist for 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, ?

2.3. Length of largest left-truncatable prime in base n for 3<=n<=36: (since no such primes exist for 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)

2.4. 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)

3. Right-truncatable prime

3.1. Largest right-truncatable prime in base n written in base 10 for 3<=n<=36: (since no such primes exist for 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

3.2. Largest right-truncatable prime in base n written in base n for 3<=n<=36: (since no such primes exist for 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

3.3. Length of largest right-truncatable prime in base n for 3<=n<=36: (since no such primes exist for 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

3.4. 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

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, ?, 249069897374447078426903207266791381270529, ?, (20^449*16-2809)/19, ?, 22^763*20+7041, (23^800873*106-7)/11, 973767003942195520947294504280890002680537875404412883659428819153939518991719953852457999342229586282557076411687300474817686178175693329, ?, ?, ?, ?, ?, 30^1023*12+1, ?, ?, ?, ?, ?, ?

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, 8032017111, 40000000000000000000000000000000000000000000000000000000000000000000000000000000000049, 96666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666608, 90354291, ?, GG0000000000000000000000000000001, ?, G44799, ?, K0760EC1, 9E800873, M666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666661, ?, ?, ?, ?, ?, C010221, ?, ?, ?, ?, ?, ?

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, (≥9896), (≥9750), (≥9961), (≥9377), (≥9599), (≥3935)

4.4. Number of minimal primes in base n for 2<=n<=36: (assuming the conjecture in https://mersenneforum.org/showpost.p...&postcount=675 is true)

2, 3, 3, 8, 7, 9, 15, 12, 26, 152, 17, 228, 240, 100, 483, 1280, 50, 3463, 651, 2601, 1242, 6021, 306, (17608 or 17609), 5664, 17215, 5784, (57296 or 57297), 220, (79199 ~ 79206), (45266 ~ 45283), (57708 or 57709), (56487 ~ 56490), (182392 or 182393), 6297

Last fiddled with by sweety439 on 2020-11-05 at 13:55
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Old 2020-11-03, 09:26   #2
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5. Repunit prime [it is conjectured that there are infinitely many repunit primes in base n, if n is not perfect power]

5.1. 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

5.2. 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, 1313, 11

5.3. 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

6. Weakly prime [it is conjectured that there are infinitely many weakly primes in base n for all n>=2]

6.1. 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, ?, 356479, ?, ?, ?, 22549349, ?

6.2. 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, ?, BTTA, ?, ?, ?, F0WM4, ?

6.3. Length of smallest weakly prime in base n written in base n for 2<=n<=36

7. Two-sided prime

7.1. Largest two-sided prime in base n written in base 10 for 3<=n<=36: (since no such primes exist for 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

7.2. Largest two-sided prime in base n written in base n for 3<=n<=36: (since no such primes exist for 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

7.3. Length of largest two-sided prime in base n for 3<=n<=36: (since no such primes exist for 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

7.4. Number of two-sided primes in base n

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

8. Circular prime (data only available for bases <=12)

8.1. 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

8.2. 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

8.3. 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

8.4. Number of circular primes in base n (repunit primes excluded) for 2<=n<=12: (conjectured)

Last fiddled with by sweety439 on 2020-11-04 at 12:33
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Old 2020-11-03, 09:29   #3
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9. Full-reptend prime [it is conjectured that there are infinitely many full-reptend primes in base n, if n is not square]

Base//Full-reptend primes

2: 3, 5, 11, 13, 19, 29, 37, 53, 59, 61, 67, 83, 101, 107, 131, 139, 149, 163, 173, 179, 181, 197, 211, 227, 269, 293, 317, 347, 349, 373, 379, 389, 419, 421, 443, 461, 467, 491, 509, 523, 541, 547, 557, 563, 587, 613, 619, 653, 659, 661, 677, 701, 709, 757, 773, 787, 797, 821, 827, 829, 853, 859, 877, 883, 907, 941, 947, 1019, 1061, 1091, 1109, 1117, 1123, 1171, 1187, 1213, 1229, 1237, 1259, 1277, 1283, 1291, 1301, 1307, 1373, 1381, 1427, 1451, 1453, 1483, 1493, 1499, 1523, 1531, 1549, 1571, 1619, 1621, 1637, 1667, 1669, 1693, 1733, 1741, 1747, 1787, 1861, 1867, 1877, 1901, 1907, 1931, 1949, 1973, 1979, 1987, 1997, 2027, 2029, 2053, 2069, 2083, 2099, 2131, 2141, 2213, 2221, 2237, 2243, 2267, 2269, 2293, 2309, 2333, 2339, 2357, 2371, 2389, 2437, 2459, 2467, 2477, 2531, 2539, 2549, 2557, 2579, 2621, 2659, 2677, 2683, 2693, 2699, 2707, 2741, 2789, 2797, 2803, 2819, 2837, 2843, 2851, 2861, 2909, 2939, 2957, 2963, 3011, 3019, 3037, 3067, 3083, 3187, 3203, 3253, 3299, 3307, 3323, 3347, 3371, 3413, 3461, 3467, 3469, 3491, 3499, 3517, 3533, 3539, 3547, 3557, 3571, 3581, 3613, 3637, 3643, 3659, 3677, 3691, 3701, 3709, 3733, 3779, 3797, 3803, 3851, 3853, 3877, 3907, 3917, 3923, 3931, 3947, 3989, 4003, 4013, 4019, 4021, 4091, 4093, ...
3: 2, 5, 7, 17, 19, 29, 31, 43, 53, 79, 89, 101, 113, 127, 137, 139, 149, 163, 173, 197, 199, 211, 223, 233, 257, 269, 281, 283, 293, 317, 331, 353, 379, 389, 401, 449, 461, 463, 487, 509, 521, 557, 569, 571, 593, 607, 617, 631, 641, 653, 677, 691, 701, 739, 751, 773, 797, 809, 811, 821, 823, 857, 859, 881, 907, 929, 941, 953, 977, 1013, 1039, 1049, 1061, 1063, 1087, 1097, 1109, 1123, 1193, 1217, 1229, 1231, 1277, 1279, 1291, 1301, 1327, 1361, 1373, 1409, 1423, 1433, 1447, 1459, 1481, 1483, 1493, 1553, 1567, 1579, 1601, 1613, 1627, 1637, 1663, 1697, 1699, 1709, 1721, 1723, 1733, 1747, 1831, 1889, 1901, 1913, 1949, 1951, 1973, 1987, 1997, 1999, 2011, 2069, 2081, 2083, 2129, 2141, 2143, 2153, 2213, 2237, 2239, 2273, 2309, 2311, 2333, 2347, 2357, 2371, 2381, 2393, 2417, 2467, 2477, 2503, 2539, 2549, 2609, 2633, 2647, 2657, 2659, 2683, 2693, 2707, 2719, 2729, 2731, 2741, 2753, 2767, 2777, 2789, 2801, 2837, 2861, 2897, 2909, 2957, 2969, 3041, 3089, 3137, 3163, 3209, 3257, 3259, 3271, 3307, 3329, 3331, 3389, 3391, 3413, 3449, 3461, 3463, 3533, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3617, 3643, 3677, 3701, 3727, 3761, 3797, 3821, 3823, 3833, 3917, 3919, 3929, 3931, 3943, 3989, 4001, 4003, 4013, 4027, 4049, 4073, ...
4: (none)
5: 2, 3, 7, 17, 23, 37, 43, 47, 53, 73, 83, 97, 103, 107, 113, 137, 157, 167, 173, 193, 197, 223, 227, 233, 257, 263, 277, 283, 293, 307, 317, 347, 353, 373, 383, 397, 433, 443, 463, 467, 503, 523, 547, 557, 563, 577, 587, 593, 607, 613, 617, 647, 653, 673, 677, 683, 727, 743, 757, 773, 787, 797, 857, 863, 877, 887, 907, 937, 947, 953, 967, 977, 983, 1013, 1033, 1093, 1097, 1103, 1153, 1163, 1187, 1193, 1213, 1217, 1223, 1237, 1277, 1283, 1307, 1327, 1367, 1373, 1427, 1433, 1483, 1487, 1493, 1523, 1543, 1553, 1567, 1583, 1607, 1613, 1637, 1663, 1667, 1693, 1697, 1733, 1747, 1777, 1787, 1823, 1847, 1877, 1907, 1913, 1933, 1987, 1993, 1997, 2003, 2017, 2027, 2053, 2063, 2083, 2087, 2113, 2143, 2153, 2203, 2207, 2213, 2237, 2243, 2267, 2273, 2293, 2297, 2333, 2347, 2357, 2377, 2383, 2393, 2417, 2423, 2437, 2447, 2467, 2473, 2477, 2503, 2543, 2557, 2617, 2633, 2647, 2657, 2663, 2677, 2683, 2687, 2693, 2713, 2753, 2767, 2777, 2797, 2833, 2837, 2843, 2887, 2897, 2903, 2917, 2927, 2957, 2963, 3023, 3037, 3067, 3083, 3163, 3167, 3187, 3203, 3217, 3253, 3307, 3323, 3343, 3347, 3373, 3407, 3413, 3433, 3463, 3467, 3517, 3527, 3533, 3547, 3557, 3583, 3593, 3607, 3613, 3617, 3623, 3643, 3673, 3677, 3697, 3767, 3793, 3797, 3803, 3833, 3847, 3863, 3907, 3917, 3923, 3943, 3947, 4003, 4007, 4013, 4027, 4057, 4073, 4093, ...
6: 11, 13, 17, 41, 59, 61, 79, 83, 89, 103, 107, 109, 113, 127, 131, 137, 151, 157, 179, 199, 223, 227, 229, 233, 251, 257, 271, 277, 347, 367, 373, 397, 401, 419, 443, 449, 467, 487, 491, 521, 563, 569, 587, 593, 613, 641, 659, 661, 683, 709, 733, 757, 761, 809, 823, 827, 829, 853, 857, 881, 929, 947, 953, 967, 971, 977, 991, 1019, 1039, 1049, 1063, 1069, 1091, 1097, 1117, 1163, 1187, 1193, 1213, 1217, 1237, 1259, 1279, 1283, 1289, 1303, 1307, 1327, 1361, 1381, 1409, 1423, 1427, 1429, 1433, 1451, 1471, 1481, 1499, 1523, 1543, 1549, 1553, 1567, 1601, 1619, 1621, 1663, 1667, 1669, 1759, 1789, 1811, 1831, 1861, 1879, 1889, 1907, 1913, 1979, 1999, 2027, 2029, 2053, 2081, 2099, 2129, 2143, 2153, 2221, 2243, 2267, 2269, 2273, 2293, 2297, 2389, 2393, 2411, 2417, 2437, 2441, 2459, 2503, 2531, 2551, 2557, 2579, 2609, 2633, 2657, 2699, 2729, 2749, 2767, 2777, 2791, 2797, 2801, 2819, 2843, 2887, 2897, 2917, 2939, 2963, 2969, 3011, 3041, 3061, 3079, 3083, 3089, 3109, 3137, 3203, 3209, 3229, 3251, 3253, 3257, 3271, 3299, 3301, 3319, 3323, 3329, 3347, 3371, 3391, 3449, 3463, 3467, 3469, 3491, 3517, 3539, 3583, 3593, 3617, 3659, 3709, 3733, 3761, 3779, 3803, 3823, 3833, 3847, 3853, 3929, 3943, 3947, 3967, 4001, 4019, 4049, 4073, 4091, 4093, ...
7: 2, 5, 11, 13, 17, 23, 41, 61, 67, 71, 79, 89, 97, 101, 107, 127, 151, 163, 173, 179, 211, 229, 239, 241, 257, 263, 269, 293, 347, 349, 359, 379, 397, 431, 433, 443, 461, 491, 499, 509, 521, 547, 577, 593, 599, 601, 631, 659, 677, 683, 733, 739, 743, 761, 773, 797, 823, 827, 857, 863, 907, 919, 929, 937, 941, 967, 991, 997, 1013, 1019, 1049, 1051, 1069, 1097, 1103, 1109, 1163, 1181, 1187, 1193, 1217, 1237, 1249, 1277, 1283, 1301, 1303, 1361, 1367, 1433, 1439, 1451, 1471, 1523, 1553, 1601, 1607, 1609, 1613, 1619, 1637, 1667, 1669, 1693, 1697, 1721, 1747, 1753, 1759, 1787, 1831, 1889, 1949, 1973, 1993, 2003, 2011, 2027, 2039, 2083, 2087, 2089, 2111, 2141, 2143, 2179, 2207, 2251, 2273, 2281, 2309, 2339, 2341, 2357, 2393, 2447, 2459, 2477, 2503, 2531, 2543, 2591, 2593, 2609, 2621, 2647, 2671, 2677, 2693, 2699, 2711, 2729, 2731, 2777, 2789, 2843, 2851, 2879, 2897, 2917, 2957, 2963, 3041, 3119, 3121, 3169, 3181, 3203, 3209, 3253, 3271, 3299, 3343, 3371, 3449, 3457, 3467, 3511, 3517, 3533, 3539, 3541, 3571, 3607, 3617, 3623, 3673, 3701, 3719, 3739, 3767, 3769, 3793, 3797, 3803, 3821, 3853, 3931, 3943, 3989, 4019, 4049, 4073, 4093, ...
8: 3, 5, 11, 29, 53, 59, 83, 101, 107, 131, 149, 173, 179, 197, 227, 269, 293, 317, 347, 389, 419, 443, 461, 467, 491, 509, 557, 563, 587, 653, 659, 677, 701, 773, 797, 821, 827, 941, 947, 1019, 1061, 1091, 1109, 1187, 1229, 1259, 1277, 1283, 1301, 1307, 1373, 1427, 1451, 1493, 1499, 1523, 1571, 1619, 1637, 1667, 1733, 1787, 1877, 1901, 1907, 1931, 1949, 1973, 1979, 1997, 2027, 2069, 2099, 2141, 2213, 2237, 2243, 2267, 2309, 2333, 2339, 2357, 2459, 2477, 2531, 2549, 2579, 2621, 2693, 2699, 2741, 2789, 2819, 2837, 2843, 2861, 2909, 2939, 2957, 2963, 3011, 3083, 3203, 3299, 3323, 3347, 3371, 3413, 3461, 3467, 3491, 3533, 3539, 3557, 3581, 3659, 3677, 3701, 3779, 3797, 3803, 3851, 3917, 3923, 3947, 3989, 4013, 4019, 4091, ...
9: 2 (no others)
10: 7, 17, 19, 23, 29, 47, 59, 61, 97, 109, 113, 131, 149, 167, 179, 181, 193, 223, 229, 233, 257, 263, 269, 313, 337, 367, 379, 383, 389, 419, 433, 461, 487, 491, 499, 503, 509, 541, 571, 577, 593, 619, 647, 659, 701, 709, 727, 743, 811, 821, 823, 857, 863, 887, 937, 941, 953, 971, 977, 983, 1019, 1021, 1033, 1051, 1063, 1069, 1087, 1091, 1097, 1103, 1109, 1153, 1171, 1181, 1193, 1217, 1223, 1229, 1259, 1291, 1297, 1301, 1303, 1327, 1367, 1381, 1429, 1433, 1447, 1487, 1531, 1543, 1549, 1553, 1567, 1571, 1579, 1583, 1607, 1619, 1621, 1663, 1697, 1709, 1741, 1777, 1783, 1789, 1811, 1823, 1847, 1861, 1873, 1913, 1949, 1979, 2017, 2029, 2063, 2069, 2099, 2113, 2137, 2141, 2143, 2153, 2179, 2207, 2221, 2251, 2269, 2273, 2297, 2309, 2339, 2341, 2371, 2383, 2389, 2411, 2417, 2423, 2447, 2459, 2473, 2539, 2543, 2549, 2579, 2593, 2617, 2621, 2633, 2657, 2663, 2687, 2699, 2713, 2731, 2741, 2753, 2767, 2777, 2789, 2819, 2833, 2851, 2861, 2887, 2897, 2903, 2909, 2927, 2939, 2971, 3011, 3019, 3023, 3137, 3167, 3221, 3251, 3257, 3259, 3299, 3301, 3313, 3331, 3343, 3371, 3389, 3407, 3433, 3461, 3463, 3469, 3527, 3539, 3571, 3581, 3593, 3607, 3617, 3623, 3659, 3673, 3701, 3709, 3727, 3767, 3779, 3821, 3833, 3847, 3863, 3943, 3967, 3989, 4007, 4019, 4051, 4057, 4073, 4091, ...
11: 2, 3, 13, 17, 23, 29, 31, 41, 47, 59, 67, 71, 73, 101, 103, 109, 149, 163, 173, 179, 197, 223, 233, 251, 277, 281, 293, 331, 367, 373, 383, 419, 443, 461, 463, 467, 487, 499, 557, 569, 587, 593, 599, 601, 613, 619, 643, 647, 673, 677, 683, 701, 719, 761, 769, 809, 821, 839, 853, 857, 863, 883, 937, 941, 947, 953, 971, 983, 991, 997, 1009, 1033, 1039, 1069, 1097, 1103, 1129, 1201, 1217, 1229, 1249, 1259, 1289, 1307, 1361, 1367, 1381, 1423, 1429, 1439, 1483, 1493, 1499, 1511, 1523, 1553, 1567, 1571, 1597, 1601, 1607, 1613, 1657, 1669, 1699, 1733, 1783, 1787, 1801, 1831, 1861, 1877, 1879, 1889, 1907, 1913, 1949, 1951, 1997, 2011, 2027, 2039, 2083, 2089, 2099, 2129, 2141, 2153, 2203, 2213, 2221, 2267, 2273, 2309, 2311, 2347, 2389, 2393, 2399, 2417, 2423, 2441, 2447, 2477, 2579, 2593, 2609, 2657, 2663, 2687, 2699, 2711, 2713, 2731, 2801, 2803, 2819, 2837, 2843, 2857, 2917, 2927, 2963, 2969, 2971, 3019, 3023, 3049, 3067, 3083, 3109, 3137, 3181, 3191, 3209, 3229, 3253, 3313, 3329, 3347, 3359, 3371, 3373, 3391, 3449, 3491, 3499, 3517, 3533, 3547, 3581, 3593, 3623, 3673, 3727, 3761, 3767, 3769, 3797, 3851, 3889, 3929, 3947, 3989, 4007, 4019, 4021, 4027, 4079, ...
12: 5, 7, 17, 31, 41, 43, 53, 67, 101, 103, 113, 127, 137, 139, 149, 151, 163, 173, 197, 223, 257, 269, 281, 283, 293, 317, 353, 367, 379, 389, 401, 449, 461, 509, 523, 547, 557, 569, 571, 593, 607, 617, 619, 631, 641, 653, 691, 701, 739, 751, 761, 773, 787, 797, 809, 821, 857, 881, 929, 953, 967, 977, 991, 1013, 1049, 1051, 1061, 1087, 1097, 1109, 1123, 1171, 1181, 1193, 1217, 1229, 1289, 1291, 1303, 1327, 1361, 1373, 1409, 1423, 1433, 1447, 1459, 1481, 1483, 1493, 1531, 1543, 1553, 1579, 1613, 1627, 1637, 1697, 1699, 1709, 1721, 1723, 1733, 1747, 1759, 1783, 1831, 1867, 1877, 1879, 1889, 1901, 1913, 1949, 1973, 1997, 1999, 2011, 2069, 2131, 2143, 2153, 2213, 2237, 2239, 2273, 2297, 2309, 2333, 2347, 2357, 2371, 2381, 2393, 2417, 2441, 2477, 2539, 2549, 2609, 2621, 2657, 2693, 2707, 2719, 2731, 2753, 2767, 2777, 2789, 2791, 2801, 2803, 2837, 2851, 2861, 2897, 2909, 2957, 2969, 3019, 3041, 3079, 3089, 3163, 3187, 3209, 3257, 3259, 3271, 3319, 3329, 3331, 3389, 3391, 3413, 3449, 3461, 3463, 3511, 3533, 3547, 3557, 3559, 3581, 3593, 3617, 3677, 3701, 3727, 3739, 3761, 3797, 3821, 3833, 3847, 3917, 3919, 3929, 3931, 3943, 3967, 3989, 4003, 4013, 4027, 4051, 4073, ...
13: 2, 5, 11, 19, 31, 37, 41, 47, 59, 67, 71, 73, 83, 89, 97, 109, 137, 149, 151, 167, 197, 227, 239, 241, 281, 293, 307, 317, 349, 353, 359, 379, 383, 397, 401, 431, 449, 457, 479, 487, 509, 541, 557, 577, 587, 593, 613, 617, 631, 643, 683, 691, 733, 743, 769, 773, 787, 811, 821, 827, 839, 863, 877, 929, 941, 947, 967, 977, 983, 1019, 1033, 1051, 1087, 1097, 1103, 1129, 1163, 1181, 1217, 1229, 1259, 1279, 1289, 1307, 1319, 1321, 1367, 1373, 1399, 1409, 1423, 1451, 1487, 1493, 1523, 1553, 1579, 1597, 1607, 1619, 1669, 1697, 1709, 1721, 1747, 1783, 1787, 1801, 1867, 1877, 1879, 1913, 1931, 1987, 1997, 2039, 2069, 2087, 2099, 2111, 2113, 2143, 2153, 2179, 2221, 2243, 2267, 2269, 2273, 2293, 2309, 2333, 2351, 2371, 2377, 2381, 2399, 2423, 2459, 2477, 2503, 2543, 2579, 2593, 2621, 2633, 2647, 2663, 2693, 2699, 2719, 2741, 2749, 2767, 2777, 2789, 2801, 2819, 2879, 2897, 2917, 2927, 2953, 2957, 2969, 2971, 3023, 3037, 3049, 3061, 3079, 3083, 3089, 3109, 3167, 3187, 3203, 3209, 3313, 3323, 3343, 3347, 3359, 3373, 3391, 3413, 3463, 3469, 3517, 3547, 3557, 3581, 3583, 3593, 3607, 3659, 3671, 3673, 3677, 3733, 3803, 3833, 3853, 3863, 3881, 3911, 3919, 3931, 3947, 3967, 3989, 4019, ...
14: 3, 17, 19, 23, 29, 53, 59, 73, 83, 89, 97, 109, 127, 131, 149, 151, 227, 239, 241, 251, 257, 263, 277, 283, 307, 313, 317, 353, 359, 373, 389, 419, 421, 431, 433, 467, 487, 521, 541, 557, 563, 587, 593, 599, 601, 613, 631, 643, 653, 701, 709, 743, 751, 757, 761, 769, 787, 821, 823, 857, 859, 863, 877, 881, 919, 929, 1031, 1049, 1087, 1091, 1093, 1097, 1103, 1117, 1123, 1153, 1193, 1213, 1217, 1229, 1249, 1259, 1291, 1303, 1307, 1361, 1367, 1373, 1427, 1433, 1439, 1453, 1471, 1489, 1493, 1531, 1549, 1553, 1571, 1583, 1601, 1607, 1627, 1663, 1697, 1699, 1709, 1721, 1733, 1753, 1789, 1831, 1867, 1871, 1877, 1889, 1901, 1907, 1931, 1933, 1979, 1993, 1997, 2039, 2053, 2069, 2087, 2089, 2099, 2111, 2113, 2131, 2143, 2203, 2207, 2237, 2243, 2267, 2269, 2273, 2281, 2371, 2393, 2411, 2423, 2437, 2441, 2447, 2543, 2549, 2579, 2593, 2609, 2617, 2659, 2671, 2741, 2777, 2797, 2819, 2837, 2879, 2897, 2909, 2927, 2939, 3001, 3041, 3061, 3083, 3109, 3119, 3169, 3209, 3221, 3229, 3271, 3301, 3307, 3323, 3331, 3343, 3413, 3433, 3449, 3457, 3491, 3499, 3511, 3547, 3557, 3581, 3607, 3613, 3617, 3623, 3637, 3643, 3659, 3677, 3719, 3733, 3767, 3779, 3847, 3917, 3923, 3943, 3947, 4003, 4013, 4049, 4073, 4091, ...
15: 2, 13, 19, 23, 29, 37, 41, 47, 73, 83, 89, 97, 101, 107, 139, 149, 151, 157, 167, 193, 199, 227, 263, 269, 271, 281, 313, 337, 347, 373, 379, 383, 389, 401, 433, 439, 449, 457, 461, 467, 499, 503, 509, 521, 563, 569, 577, 587, 613, 619, 631, 641, 647, 683, 691, 701, 733, 743, 751, 757, 809, 821, 827, 863, 881, 887, 919, 929, 947, 983, 1039, 1049, 1061, 1093, 1103, 1109, 1153, 1181, 1187, 1223, 1229, 1279, 1283, 1289, 1291, 1297, 1301, 1307, 1367, 1399, 1409, 1427, 1459, 1471, 1481, 1487, 1523, 1583, 1657, 1667, 1699, 1709, 1753, 1787, 1823, 1847, 1873, 1879, 1889, 1901, 1907, 1933, 1949, 1951, 1999, 2003, 2017, 2027, 2063, 2069, 2087, 2131, 2137, 2141, 2179, 2207, 2239, 2243, 2251, 2267, 2293, 2309, 2381, 2423, 2437, 2441, 2447, 2543, 2549, 2557, 2593, 2609, 2617, 2663, 2671, 2677, 2687, 2713, 2719, 2731, 2741, 2789, 2791, 2797, 2843, 2861, 2903, 2909, 2917, 2953, 2963, 2969, 3019, 3023, 3041, 3083, 3089, 3167, 3203, 3209, 3217, 3221, 3253, 3271, 3313, 3319, 3323, 3329, 3347, 3373, 3407, 3449, 3457, 3461, 3467, 3517, 3527, 3581, 3613, 3623, 3631, 3637, 3673, 3701, 3739, 3761, 3767, 3803, 3821, 3863, 3881, 3919, 3923, 3929, 3931, 3947, 3989, 4001, 4007, 4049, 4051, 4057, 4093, ...
16: (none)
17: 2, 3, 5, 7, 11, 23, 31, 37, 41, 61, 97, 107, 113, 131, 139, 167, 173, 193, 197, 211, 227, 233, 269, 277, 283, 311, 313, 317, 347, 367, 379, 401, 419, 431, 439, 449, 479, 487, 499, 503, 521, 547, 571, 607, 617, 641, 643, 653, 673, 677, 683, 691, 709, 719, 743, 751, 787, 809, 821, 823, 827, 839, 853, 857, 881, 887, 907, 911, 929, 941, 983, 997, 1009, 1013, 1049, 1051, 1091, 1117, 1129, 1151, 1153, 1163, 1187, 1193, 1201, 1217, 1229, 1297, 1319, 1367, 1433, 1439, 1451, 1493, 1499, 1523, 1553, 1567, 1601, 1609, 1621, 1627, 1637, 1669, 1693, 1697, 1723, 1847, 1877, 1901, 1907, 1931, 1949, 1979, 1999, 2011, 2029, 2063, 2069, 2081, 2111, 2113, 2153, 2207, 2213, 2251, 2267, 2273, 2309, 2339, 2357, 2383, 2411, 2417, 2441, 2459, 2477, 2521, 2539, 2543, 2557, 2579, 2621, 2647, 2657, 2659, 2663, 2693, 2713, 2749, 2777, 2819, 2879, 2887, 2897, 2917, 2953, 2963, 2969, 2999, 3019, 3023, 3037, 3083, 3089, 3121, 3167, 3169, 3191, 3203, 3253, 3257, 3259, 3301, 3359, 3371, 3373, 3389, 3407, 3457, 3461, 3491, 3529, 3533, 3539, 3581, 3593, 3677, 3701, 3733, 3767, 3769, 3779, 3797, 3803, 3847, 3881, 3907, 3917, 3947, 3967, 3989, 4001, 4007, 4019, 4049, 4051, 4057, 4073, ...
18: 5, 11, 29, 37, 43, 53, 59, 61, 67, 83, 101, 107, 109, 139, 149, 157, 163, 173, 179, 181, 197, 227, 251, 269, 277, 283, 293, 317, 347, 349, 379, 389, 397, 419, 421, 461, 467, 491, 509, 523, 541, 547, 557, 563, 571, 587, 613, 619, 653, 659, 661, 677, 683, 691, 701, 733, 739, 757, 773, 787, 797, 811, 821, 827, 853, 859, 877, 941, 947, 971, 1013, 1019, 1051, 1069, 1091, 1109, 1117, 1123, 1163, 1171, 1181, 1187, 1229, 1277, 1283, 1301, 1307, 1453, 1459, 1483, 1493, 1499, 1523, 1549, 1571, 1579, 1613, 1619, 1621, 1627, 1637, 1669, 1693, 1699, 1709, 1723, 1733, 1741, 1747, 1787, 1789, 1811, 1861, 1867, 1877, 1901, 1907, 1931, 1949, 1973, 1979, 1997, 2003, 2011, 2027, 2029, 2069, 2099, 2131, 2141, 2213, 2221, 2237, 2243, 2267, 2269, 2309, 2333, 2339, 2347, 2357, 2381, 2389, 2411, 2459, 2477, 2539, 2549, 2579, 2621, 2677, 2693, 2699, 2707, 2731, 2741, 2749, 2789, 2803, 2819, 2837, 2843, 2851, 2861, 2909, 2917, 2939, 2957, 2963, 3019, 3061, 3067, 3083, 3109, 3163, 3187, 3203, 3229, 3253, 3259, 3299, 3323, 3331, 3347, 3371, 3389, 3413, 3461, 3467, 3491, 3499, 3517, 3533, 3539, 3541, 3547, 3557, 3571, 3581, 3613, 3637, 3659, 3677, 3733, 3739, 3779, 3803, 3821, 3851, 3853, 3877, 3907, 3923, 3931, 3947, 3989, 4003, 4013, 4021, 4027, 4051, 4093, ...
19: 2, 7, 11, 13, 23, 29, 37, 41, 43, 47, 53, 83, 89, 113, 139, 163, 173, 191, 193, 239, 251, 257, 263, 269, 281, 293, 311, 317, 337, 347, 359, 367, 401, 419, 433, 443, 449, 463, 467, 479, 491, 499, 503, 509, 521, 569, 571, 587, 601, 619, 631, 641, 643, 647, 673, 677, 719, 727, 739, 773, 797, 829, 857, 877, 883, 919, 941, 947, 953, 967, 977, 1093, 1097, 1103, 1153, 1163, 1187, 1193, 1223, 1229, 1237, 1249, 1259, 1321, 1361, 1381, 1409, 1423, 1433, 1451, 1481, 1487, 1499, 1543, 1549, 1553, 1559, 1583, 1607, 1619, 1637, 1693, 1709, 1741, 1777, 1783, 1787, 1789, 1801, 1847, 1861, 1871, 1877, 1879, 1889, 1907, 1913, 1933, 1987, 1997, 1999, 2011, 2017, 2029, 2039, 2063, 2081, 2099, 2141, 2237, 2243, 2267, 2269, 2273, 2287, 2309, 2333, 2377, 2399, 2411, 2521, 2543, 2549, 2551, 2591, 2617, 2671, 2689, 2693, 2699, 2707, 2729, 2749, 2777, 2789, 2801, 2819, 2833, 2851, 2909, 2917, 2927, 2953, 2957, 2971, 2999, 3011, 3079, 3083, 3109, 3137, 3163, 3169, 3203, 3221, 3229, 3257, 3301, 3323, 3373, 3391, 3407, 3413, 3449, 3461, 3467, 3529, 3533, 3539, 3593, 3607, 3613, 3637, 3659, 3671, 3677, 3691, 3701, 3761, 3767, 3779, 3793, 3821, 3823, 3847, 3853, 3863, 3889, 3911, 3917, 3923, 3929, 3989, 4007, 4021, 4049, 4091, 4093, ...
20: 3, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 103, 107, 113, 137, 157, 163, 167, 173, 223, 227, 233, 257, 263, 277, 283, 293, 313, 317, 337, 347, 353, 367, 383, 397, 433, 443, 463, 467, 487, 503, 547, 557, 563, 587, 593, 607, 613, 647, 653, 673, 677, 683, 727, 743, 773, 797, 823, 853, 857, 863, 887, 907, 953, 977, 983, 1013, 1063, 1087, 1093, 1097, 1103, 1117, 1123, 1163, 1187, 1193, 1213, 1217, 1223, 1237, 1277, 1283, 1297, 1303, 1307, 1327, 1367, 1373, 1427, 1433, 1447, 1483, 1487, 1493, 1523, 1553, 1607, 1613, 1637, 1667, 1697, 1733, 1747, 1777, 1787, 1823, 1847, 1867, 1877, 1907, 1913, 1933, 1973, 1987, 1993, 1997, 2003, 2017, 2027, 2053, 2063, 2087, 2113, 2137, 2143, 2153, 2203, 2207, 2213, 2243, 2267, 2273, 2297, 2333, 2347, 2357, 2377, 2383, 2393, 2417, 2423, 2447, 2467, 2477, 2503, 2543, 2593, 2647, 2657, 2663, 2677, 2683, 2687, 2693, 2707, 2753, 2767, 2777, 2803, 2833, 2837, 2843, 2897, 2903, 2917, 2927, 2957, 2963, 3023, 3037, 3083, 3137, 3163, 3167, 3187, 3203, 3217, 3253, 3257, 3313, 3323, 3343, 3347, 3373, 3413, 3463, 3467, 3527, 3533, 3557, 3583, 3593, 3607, 3613, 3617, 3623, 3637, 3677, 3697, 3727, 3733, 3767, 3793, 3797, 3803, 3833, 3853, 3863, 3877, 3917, 3923, 3943, 3947, 3967, 4007, 4013, 4027, 4057, 4073, ...
21: 2, 19, 23, 29, 31, 53, 71, 97, 103, 107, 113, 137, 139, 149, 157, 179, 181, 191, 197, 223, 233, 239, 263, 271, 281, 307, 313, 317, 347, 359, 389, 397, 401, 409, 431, 443, 449, 491, 523, 557, 569, 577, 607, 619, 643, 653, 659, 683, 701, 727, 733, 743, 769, 787, 809, 811, 821, 827, 829, 863, 911, 937, 947, 977, 997, 1019, 1031, 1061, 1063, 1103, 1123, 1153, 1163, 1187, 1229, 1237, 1249, 1279, 1283, 1289, 1321, 1367, 1399, 1439, 1447, 1459, 1483, 1489, 1493, 1499, 1523, 1609, 1619, 1627, 1657, 1667, 1669, 1699, 1709, 1733, 1741, 1753, 1777, 1787, 1861, 1867, 1877, 1879, 1913, 1993, 1997, 2027, 2039, 2081, 2087, 2111, 2129, 2153, 2203, 2207, 2213, 2237, 2239, 2287, 2297, 2333, 2339, 2341, 2381, 2417, 2423, 2447, 2459, 2539, 2543, 2549, 2591, 2593, 2633, 2657, 2659, 2699, 2707, 2741, 2749, 2753, 2801, 2803, 2833, 2837, 2843, 2879, 2887, 2909, 2953, 2963, 2969, 3037, 3079, 3089, 3119, 3137, 3163, 3203, 3221, 3253, 3257, 3299, 3307, 3329, 3347, 3413, 3457, 3463, 3467, 3517, 3539, 3547, 3559, 3581, 3583, 3593, 3623, 3631, 3643, 3677, 3709, 3719, 3727, 3767, 3803, 3833, 3851, 3853, 3917, 3919, 3929, 3967, 4001, 4013, 4019, 4021, 4051, 4093, ...
22: 5, 17, 19, 31, 37, 41, 47, 53, 71, 83, 107, 131, 139, 191, 193, 199, 211, 223, 227, 233, 269, 281, 283, 307, 311, 317, 337, 347, 367, 383, 389, 397, 409, 421, 487, 491, 509, 523, 547, 563, 569, 593, 599, 601, 647, 653, 659, 709, 719, 739, 761, 773, 787, 797, 809, 823, 827, 829, 839, 857, 863, 953, 983, 991, 1009, 1019, 1021, 1033, 1039, 1051, 1061, 1087, 1091, 1097, 1103, 1109, 1129, 1163, 1187, 1201, 1217, 1237, 1277, 1279, 1283, 1289, 1297, 1301, 1303, 1361, 1367, 1373, 1423, 1427, 1439, 1451, 1453, 1459, 1481, 1511, 1531, 1543, 1549, 1553, 1567, 1607, 1619, 1637, 1657, 1667, 1709, 1741, 1777, 1811, 1831, 1889, 1901, 1913, 1931, 1973, 1979, 1993, 2029, 2039, 2069, 2089, 2129, 2153, 2237, 2243, 2273, 2293, 2333, 2339, 2357, 2371, 2381, 2393, 2399, 2411, 2417, 2441, 2447, 2459, 2521, 2609, 2617, 2621, 2657, 2659, 2663, 2677, 2683, 2687, 2693, 2713, 2797, 2801, 2857, 2887, 2909, 2927, 2939, 2957, 2969, 3011, 3023, 3037, 3049, 3061, 3137, 3163, 3203, 3221, 3251, 3299, 3329, 3359, 3361, 3389, 3391, 3413, 3449, 3467, 3469, 3539, 3593, 3623, 3643, 3659, 3673, 3677, 3701, 3719, 3727, 3733, 3739, 3761, 3767, 3779, 3803, 3821, 3853, 3889, 3907, 3917, 3919, 3923, 3929, 4001, 4003, 4007, 4013, 4079, 4091, ...
23: 2, 3, 5, 17, 47, 59, 89, 97, 113, 127, 131, 137, 149, 167, 179, 181, 223, 229, 281, 293, 307, 311, 337, 347, 389, 401, 421, 433, 439, 443, 457, 487, 491, 499, 521, 547, 557, 569, 587, 599, 607, 617, 641, 647, 661, 677, 683, 709, 719, 733, 739, 769, 773, 797, 811, 823, 863, 881, 883, 887, 947, 953, 977, 991, 1033, 1049, 1051, 1069, 1109, 1151, 1163, 1193, 1213, 1217, 1223, 1229, 1231, 1283, 1291, 1319, 1321, 1327, 1427, 1433, 1439, 1451, 1493, 1499, 1511, 1543, 1559, 1567, 1601, 1619, 1693, 1709, 1721, 1783, 1787, 1823, 1861, 1867, 1871, 1877, 1879, 1949, 1979, 1987, 1993, 1997, 2027, 2029, 2063, 2069, 2081, 2099, 2111, 2113, 2137, 2153, 2161, 2203, 2213, 2239, 2243, 2267, 2273, 2297, 2333, 2339, 2357, 2371, 2389, 2423, 2437, 2447, 2467, 2521, 2539, 2543, 2549, 2579, 2609, 2621, 2633, 2647, 2663, 2671, 2699, 2707, 2713, 2729, 2777, 2797, 2819, 2857, 2879, 2897, 2909, 2939, 2999, 3001, 3019, 3041, 3083, 3089, 3163, 3167, 3181, 3187, 3203, 3217, 3251, 3253, 3257, 3259, 3307, 3329, 3343, 3359, 3449, 3461, 3463, 3469, 3491, 3499, 3517, 3527, 3533, 3593, 3623, 3659, 3677, 3701, 3719, 3733, 3739, 3767, 3769, 3803, 3833, 3847, 3881, 3911, 3917, 3923, 3929, 3989, 4001, 4003, 4013, 4021, 4079, 4093, ...
24: 7, 11, 13, 17, 31, 37, 41, 59, 83, 89, 107, 109, 113, 137, 157, 179, 181, 223, 227, 229, 233, 251, 257, 277, 281, 347, 353, 373, 397, 401, 419, 421, 443, 463, 467, 487, 491, 541, 563, 569, 587, 593, 607, 617, 641, 683, 709, 733, 751, 761, 809, 823, 829, 857, 877, 881, 929, 947, 953, 971, 977, 1019, 1039, 1049, 1063, 1069, 1087, 1091, 1097, 1163, 1187, 1193, 1213, 1217, 1231, 1237, 1259, 1279, 1283, 1289, 1307, 1327, 1361, 1409, 1423, 1427, 1429, 1433, 1447, 1453, 1471, 1499, 1523, 1553, 1567, 1571, 1601, 1619, 1663, 1667, 1693, 1697, 1721, 1741, 1787, 1789, 1811, 1889, 1907, 1913, 1931, 1951, 1979, 1999, 2003, 2027, 2053, 2099, 2129, 2143, 2153, 2239, 2243, 2267, 2273, 2293, 2297, 2311, 2339, 2393, 2411, 2417, 2437, 2441, 2459, 2503, 2551, 2557, 2579, 2609, 2633, 2647, 2657, 2677, 2699, 2719, 2729, 2749, 2753, 2767, 2777, 2791, 2797, 2819, 2843, 2887, 2897, 2917, 2939, 2963, 2969, 3037, 3041, 3061, 3083, 3089, 3137, 3203, 3209, 3229, 3251, 3257, 3271, 3299, 3301, 3323, 3329, 3347, 3371, 3449, 3463, 3467, 3469, 3491, 3539, 3541, 3559, 3583, 3593, 3617, 3637, 3659, 3709, 3727, 3761, 3779, 3803, 3823, 3833, 3851, 3877, 3919, 3923, 3929, 3943, 3947, 4001, 4019, 4021, 4049, 4073, ...
25: 2 (no others)
26: 3, 7, 29, 41, 43, 47, 53, 61, 73, 89, 97, 101, 107, 131, 137, 139, 157, 167, 173, 179, 193, 239, 251, 269, 271, 281, 283, 347, 353, 359, 373, 383, 389, 409, 419, 443, 449, 457, 463, 467, 479, 491, 563, 593, 617, 631, 653, 659, 701, 743, 761, 797, 829, 839, 863, 883, 929, 977, 983, 997, 1009, 1013, 1033, 1069, 1091, 1093, 1097, 1103, 1109, 1117, 1129, 1151, 1171, 1187, 1201, 1213, 1217, 1277, 1279, 1283, 1289, 1301, 1319, 1367, 1381, 1399, 1409, 1423, 1427, 1453, 1459, 1483, 1487, 1489, 1553, 1601, 1607, 1613, 1637, 1667, 1693, 1697, 1699, 1733, 1741, 1811, 1879, 1907, 1913, 1949, 1973, 1979, 2003, 2011, 2017, 2027, 2039, 2083, 2087, 2111, 2113, 2131, 2137, 2141, 2143, 2153, 2237, 2273, 2351, 2357, 2399, 2423, 2467, 2503, 2531, 2539, 2543, 2549, 2593, 2633, 2657, 2663, 2677, 2711, 2767, 2777, 2837, 2843, 2861, 2879, 2897, 2909, 2927, 2939, 2953, 2963, 3001, 3019, 3023, 3049, 3079, 3089, 3163, 3167, 3191, 3209, 3217, 3251, 3257, 3259, 3301, 3331, 3343, 3359, 3371, 3389, 3391, 3461, 3463, 3467, 3529, 3533, 3539, 3593, 3607, 3613, 3697, 3779, 3797, 3821, 3833, 3851, 3863, 3881, 3911, 3917, 3919, 3923, 4003, 4013, 4021, 4049, 4091, ...
27: 2, 5, 17, 29, 53, 89, 101, 113, 137, 149, 173, 197, 233, 257, 269, 281, 293, 317, 353, 389, 401, 449, 461, 509, 521, 557, 569, 593, 617, 641, 653, 677, 701, 773, 797, 809, 821, 857, 881, 929, 941, 953, 977, 1013, 1049, 1061, 1097, 1109, 1193, 1217, 1229, 1277, 1301, 1361, 1373, 1409, 1433, 1481, 1493, 1553, 1601, 1613, 1637, 1697, 1709, 1721, 1733, 1889, 1901, 1913, 1949, 1973, 1997, 2069, 2081, 2129, 2141, 2153, 2213, 2237, 2273, 2309, 2333, 2357, 2381, 2393, 2417, 2477, 2549, 2609, 2633, 2657, 2693, 2729, 2741, 2753, 2777, 2789, 2801, 2837, 2861, 2897, 2909, 2957, 2969, 3041, 3089, 3137, 3209, 3257, 3329, 3389, 3413, 3449, 3461, 3533, 3557, 3581, 3593, 3617, 3677, 3701, 3761, 3797, 3821, 3833, 3917, 3929, 3989, 4001, 4013, 4049, 4073, ...
28: 5, 11, 13, 17, 23, 41, 43, 67, 71, 73, 79, 89, 101, 107, 173, 179, 181, 191, 229, 257, 263, 269, 293, 313, 331, 347, 353, 359, 379, 397, 409, 431, 433, 443, 461, 463, 487, 491, 499, 509, 521, 571, 577, 593, 599, 659, 661, 677, 683, 733, 739, 743, 751, 769, 773, 797, 827, 829, 853, 857, 863, 881, 883, 907, 919, 929, 937, 941, 947, 967, 991, 997, 1013, 1019, 1031, 1049, 1069, 1087, 1097, 1103, 1109, 1153, 1163, 1181, 1187, 1193, 1217, 1277, 1283, 1301, 1321, 1367, 1433, 1439, 1489, 1499, 1523, 1553, 1583, 1601, 1607, 1609, 1613, 1619, 1637, 1663, 1667, 1669, 1693, 1697, 1741, 1753, 1759, 1787, 1871, 1889, 1949, 1973, 2003, 2011, 2027, 2029, 2039, 2089, 2111, 2113, 2141, 2143, 2161, 2179, 2207, 2251, 2273, 2309, 2311, 2357, 2393, 2423, 2441, 2447, 2459, 2477, 2503, 2531, 2543, 2591, 2609, 2617, 2621, 2671, 2683, 2693, 2699, 2711, 2729, 2731, 2777, 2789, 2843, 2861, 2879, 2897, 2917, 2927, 2957, 2963, 3011, 3019, 3037, 3041, 3067, 3119, 3181, 3187, 3203, 3209, 3271, 3299, 3319, 3343, 3347, 3371, 3433, 3449, 3457, 3461, 3467, 3533, 3539, 3541, 3607, 3617, 3623, 3673, 3701, 3709, 3769, 3793, 3797, 3803, 3821, 3847, 3851, 3877, 3907, 3943, 3989, 4019, 4049, 4073, ...
29: 2, 3, 11, 17, 19, 41, 43, 47, 73, 79, 89, 97, 101, 113, 127, 131, 137, 163, 191, 211, 229, 251, 263, 269, 293, 307, 311, 317, 331, 337, 359, 389, 409, 433, 443, 449, 461, 467, 479, 491, 503, 563, 569, 599, 601, 607, 653, 659, 677, 739, 743, 751, 769, 773, 797, 809, 827, 839, 853, 859, 887, 907, 911, 947, 971, 983, 997, 1013, 1033, 1063, 1087, 1091, 1117, 1123, 1129, 1163, 1181, 1187, 1201, 1229, 1237, 1249, 1279, 1291, 1297, 1303, 1307, 1319, 1361, 1373, 1409, 1429, 1433, 1439, 1447, 1453, 1471, 1481, 1487, 1489, 1493, 1511, 1523, 1549, 1583, 1597, 1607, 1609, 1613, 1667, 1693, 1697, 1709, 1721, 1723, 1759, 1777, 1787, 1867, 1877, 1931, 1933, 1951, 1999, 2003, 2011, 2027, 2069, 2099, 2129, 2143, 2207, 2243, 2251, 2273, 2293, 2309, 2339, 2347, 2351, 2357, 2381, 2393, 2399, 2417, 2447, 2467, 2473, 2477, 2531, 2579, 2591, 2593, 2657, 2671, 2689, 2699, 2707, 2711, 2741, 2753, 2767, 2801, 2803, 2857, 2861, 2879, 2897, 2903, 2917, 2939, 2999, 3001, 3089, 3169, 3209, 3217, 3221, 3251, 3323, 3343, 3347, 3433, 3449, 3463, 3469, 3491, 3499, 3511, 3517, 3527, 3557, 3581, 3593, 3617, 3623, 3637, 3671, 3673, 3691, 3701, 3727, 3733, 3739, 3767, 3797, 3889, 3917, 3923, 3929, 3947, 4013, 4019, 4049, 4079, 4091, ...
30: 11, 23, 41, 43, 47, 59, 61, 79, 89, 109, 131, 151, 167, 173, 179, 193, 197, 199, 251, 263, 281, 293, 307, 317, 349, 383, 419, 421, 433, 439, 449, 457, 491, 503, 521, 523, 541, 557, 569, 577, 641, 647, 653, 659, 673, 677, 743, 751, 761, 773, 787, 797, 809, 829, 863, 881, 887, 907, 919, 929, 937, 971, 983, 1013, 1019, 1021, 1033, 1039, 1049, 1069, 1091, 1103, 1223, 1231, 1361, 1367, 1373, 1399, 1409, 1429, 1451, 1471, 1481, 1483, 1487, 1493, 1499, 1549, 1571, 1583, 1601, 1607, 1613, 1619, 1627, 1637, 1657, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1811, 1823, 1831, 1847, 1861, 1867, 1873, 1877, 1889, 1931, 1973, 1979, 1987, 1993, 1997, 1999, 2017, 2029, 2063, 2081, 2087, 2099, 2129, 2137, 2203, 2207, 2213, 2237, 2269, 2311, 2333, 2339, 2341, 2347, 2357, 2377, 2389, 2411, 2423, 2441, 2447, 2459, 2467, 2473, 2477, 2531, 2543, 2551, 2579, 2593, 2609, 2617, 2663, 2683, 2687, 2693, 2699, 2713, 2729, 2749, 2801, 2803, 2819, 2837, 2857, 2903, 2927, 2939, 2953, 2957, 2969, 3023, 3041, 3061, 3079, 3089, 3163, 3167, 3181, 3209, 3229, 3251, 3271, 3299, 3313, 3329, 3407, 3413, 3433, 3449, 3457, 3491, 3511, 3527, 3533, 3539, 3547, 3557, 3559, 3623, 3659, 3677, 3697, 3709, 3761, 3767, 3779, 3793, 3797, 3863, 3881, 3907, 3917, 3919, 3929, 4001, 4003, 4007, 4013, 4019, 4021, 4049, 4057, ...
31: 2, 7, 17, 29, 47, 53, 59, 61, 67, 71, 73, 89, 107, 131, 137, 197, 227, 229, 241, 269, 277, 283, 307, 311, 313, 337, 353, 359, 379, 389, 401, 419, 431, 433, 439, 443, 449, 457, 461, 467, 479, 503, 509, 557, 563, 569, 599, 607, 673, 677, 683, 709, 727, 751, 757, 761, 773, 797, 809, 811, 821, 839, 881, 887, 907, 919, 929, 941, 971, 1009, 1013, 1021, 1039, 1049, 1051, 1063, 1087, 1097, 1103, 1109, 1151, 1153, 1163, 1181, 1187, 1193, 1201, 1223, 1259, 1277, 1279, 1297, 1303, 1307, 1327, 1399, 1423, 1427, 1451, 1453, 1459, 1481, 1523, 1549, 1553, 1559, 1583, 1619, 1669, 1697, 1787, 1801, 1823, 1831, 1847, 1867, 1877, 1879, 1907, 1913, 1931, 1949, 1997, 2003, 2069, 2087, 2089, 2137, 2161, 2203, 2213, 2239, 2267, 2269, 2293, 2297, 2309, 2339, 2377, 2393, 2417, 2423, 2441, 2459, 2467, 2473, 2539, 2543, 2551, 2557, 2591, 2617, 2621, 2633, 2657, 2663, 2671, 2693, 2699, 2707, 2711, 2741, 2749, 2767, 2789, 2801, 2887, 2903, 2909, 2939, 2957, 2963, 2969, 3023, 3037, 3041, 3079, 3083, 3119, 3121, 3137, 3167, 3203, 3253, 3271, 3313, 3319, 3329, 3331, 3361, 3407, 3413, 3433, 3491, 3511, 3529, 3533, 3539, 3557, 3559, 3583, 3613, 3617, 3631, 3659, 3673, 3691, 3701, 3733, 3739, 3767, 3779, 3793, 3797, 3823, 3863, 3881, 3907, 3911, 3917, 3929, 3931, 3947, 3989, 4003, 4007, 4019, 4021, 4027, 4057, 4073, 4079, ...
32: 3, 5, 13, 19, 29, 37, 53, 59, 67, 83, 107, 139, 149, 163, 173, 179, 197, 227, 269, 293, 317, 347, 349, 373, 379, 389, 419, 443, 467, 509, 523, 547, 557, 563, 587, 613, 619, 653, 659, 677, 709, 757, 773, 787, 797, 827, 829, 853, 859, 877, 883, 907, 947, 1019, 1109, 1117, 1123, 1187, 1213, 1229, 1237, 1259, 1277, 1283, 1307, 1373, 1427, 1453, 1483, 1493, 1499, 1523, 1549, 1619, 1637, 1667, 1669, 1693, 1733, 1747, 1787, 1867, 1877, 1907, 1949, 1973, 1979, 1987, 1997, 2027, 2029, 2053, 2069, 2083, 2099, 2213, 2237, 2243, 2267, 2269, 2293, 2309, 2333, 2339, 2357, 2389, 2437, 2459, 2467, 2477, 2539, 2549, 2557, 2579, 2659, 2677, 2683, 2693, 2699, 2707, 2789, 2797, 2803, 2819, 2837, 2843, 2909, 2939, 2957, 2963, 3019, 3037, 3067, 3083, 3187, 3203, 3253, 3299, 3307, 3323, 3347, 3413, 3467, 3469, 3499, 3517, 3533, 3539, 3547, 3557, 3613, 3637, 3643, 3659, 3677, 3709, 3733, 3779, 3797, 3803, 3853, 3877, 3907, 3917, 3923, 3947, 3989, 4003, 4013, 4019, 4093, ...
33: 2, 5, 7, 13, 19, 23, 43, 47, 53, 59, 71, 73, 89, 113, 137, 179, 191, 251, 257, 269, 311, 317, 337, 349, 353, 383, 389, 409, 419, 439, 443, 449, 457, 467, 509, 547, 571, 587, 599, 601, 613, 617, 641, 647, 653, 683, 719, 733, 739, 773, 787, 797, 811, 839, 853, 863, 877, 911, 919, 929, 937, 971, 977, 983, 997, 1009, 1013, 1049, 1051, 1061, 1063, 1069, 1103, 1109, 1129, 1181, 1193, 1201, 1231, 1249, 1259, 1297, 1301, 1307, 1327, 1367, 1373, 1409, 1429, 1433, 1439, 1459, 1471, 1511, 1523, 1531, 1571, 1579, 1597, 1607, 1627, 1637, 1663, 1669, 1693, 1697, 1709, 1721, 1759, 1777, 1787, 1789, 1801, 1861, 1867, 1901, 1907, 1973, 1993, 1999, 2003, 2027, 2039, 2053, 2069, 2099, 2131, 2221, 2237, 2239, 2287, 2297, 2333, 2357, 2381, 2389, 2399, 2437, 2447, 2503, 2551, 2579, 2621, 2633, 2659, 2683, 2687, 2693, 2713, 2719, 2729, 2749, 2753, 2767, 2777, 2819, 2833, 2843, 2851, 2861, 2897, 2909, 2927, 2957, 2963, 3023, 3041, 3049, 3079, 3083, 3089, 3109, 3181, 3191, 3221, 3229, 3253, 3257, 3323, 3343, 3347, 3359, 3371, 3373, 3413, 3491, 3511, 3517, 3541, 3557, 3559, 3583, 3607, 3617, 3623, 3637, 3643, 3673, 3677, 3709, 3719, 3767, 3833, 3851, 3889, 3907, 3917, 3947, 3967, 4003, 4007, 4013, 4019, 4049, 4073, 4079, ...
34: 19, 23, 31, 41, 43, 53, 59, 67, 73, 79, 83, 101, 113, 149, 157, 167, 179, 193, 199, 233, 241, 251, 293, 311, 313, 337, 349, 367, 373, 389, 401, 431, 439, 449, 461, 467, 479, 491, 503, 509, 523, 557, 563, 587, 601, 613, 617, 641, 659, 661, 673, 701, 719, 733, 739, 743, 773, 797, 809, 839, 857, 881, 883, 887, 911, 929, 971, 983, 991, 1009, 1019, 1021, 1031, 1049, 1109, 1151, 1153, 1181, 1193, 1201, 1217, 1231, 1237, 1259, 1277, 1283, 1289, 1301, 1303, 1307, 1319, 1367, 1373, 1423, 1427, 1433, 1439, 1453, 1489, 1549, 1553, 1559, 1567, 1579, 1597, 1609, 1613, 1619, 1663, 1667, 1697, 1709, 1733, 1787, 1789, 1811, 1861, 1873, 1973, 1987, 1997, 1999, 2027, 2063, 2081, 2083, 2099, 2111, 2137, 2141, 2153, 2207, 2239, 2243, 2269, 2273, 2281, 2293, 2333, 2347, 2371, 2383, 2417, 2441, 2467, 2521, 2543, 2549, 2591, 2657, 2663, 2689, 2707, 2713, 2741, 2777, 2789, 2791, 2797, 2803, 2837, 2843, 2879, 2887, 2897, 2909, 2927, 2939, 2953, 2957, 2969, 2971, 2999, 3023, 3049, 3061, 3089, 3121, 3163, 3167, 3169, 3187, 3221, 3229, 3251, 3271, 3299, 3307, 3323, 3329, 3331, 3347, 3359, 3361, 3407, 3413, 3457, 3467, 3469, 3517, 3557, 3559, 3571, 3593, 3637, 3659, 3769, 3821, 3877, 3881, 3923, 4001, 4003, 4007, 4013, 4021, 4027, 4049, 4057, 4073, 4093, ...
35: 2, 3, 11, 37, 41, 47, 53, 61, 71, 79, 83, 89, 101, 103, 137, 151, 167, 179, 191, 197, 211, 223, 227, 229, 233, 239, 241, 269, 283, 317, 331, 359, 373, 379, 383, 409, 431, 457, 461, 467, 499, 503, 509, 521, 557, 563, 571, 587, 599, 601, 607, 617, 643, 647, 653, 659, 661, 673, 727, 739, 751, 757, 787, 829, 877, 881, 887, 911, 929, 941, 953, 977, 983, 1019, 1021, 1031, 1033, 1049, 1063, 1109, 1117, 1171, 1223, 1297, 1301, 1307, 1321, 1361, 1373, 1427, 1439, 1451, 1453, 1487, 1489, 1493, 1499, 1543, 1579, 1601, 1609, 1619, 1627, 1669, 1721, 1733, 1741, 1759, 1783, 1823, 1831, 1847, 1867, 1871, 1877, 1889, 1907, 1913, 1949, 1987, 1997, 1999, 2011, 2017, 2029, 2039, 2053, 2063, 2111, 2141, 2153, 2161, 2203, 2237, 2243, 2267, 2287, 2297, 2309, 2333, 2339, 2341, 2383, 2417, 2437, 2459, 2467, 2473, 2531, 2591, 2609, 2621, 2633, 2657, 2663, 2671, 2687, 2699, 2707, 2711, 2713, 2729, 2753, 2789, 2797, 2803, 2837, 2851, 2861, 2879, 2887, 2903, 3019, 3023, 3041, 3083, 3119, 3121, 3137, 3163, 3167, 3169, 3209, 3217, 3257, 3259, 3299, 3307, 3313, 3323, 3371, 3407, 3413, 3449, 3463, 3511, 3527, 3539, 3541, 3547, 3557, 3583, 3593, 3643, 3677, 3697, 3701, 3719, 3727, 3821, 3833, 3851, 3863, 3881, 3917, 3923, 3947, 3967, 3989, 4003, 4007, 4013, 4019, 4021, 4049, ...
36: (none)

10. Unique prime [it is conjectured that there are infinitely many unique primes in base n for all n>=2]

Base//Period length of unique primes

2 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 27, 30, 31, 32, 33, 34, 38, 40, 42, 46, 49, 54, 56, 61, 62, 65, 69, 77, 78, 80, 85, 86, 89, 90, 93, 98, 107, 120, 122, 126, 127, 129, 133, 145, 147, 150, 158, 165, 170, 174, 184, 192, 195, 202, 208, 234, 254, 261, 280, 296, 312, 322, 334, 342, 345, 366, 374, 382, 398, 410, 414, 425, 447, 471, 507, 521, 550, 567, 579, 590, 600, 602, 607, 626, 690, 694, 712, 745, 795, 816, 889, 897, 909, 954, 990, 1106, 1192, 1224, 1230, 1279, 1384, 1386, 1402, 1464, 1512, 1554, 1562, 1600, 1670, 1683, 1727, 1781, 1834, 1904, 1990, 1992, 2008, 2037, 2203, 2281, 2298, 2353, 2406, 2456, 2499, 2536, 2838, 3006, 3074, 3217, 3415, 3418, 3481, 3766, 3817, 3927, ...
3 1, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 20, 21, 24, 26, 32, 33, 36, 40, 46, 60, 63, 64, 70, 71, 72, 86, 103, 108, 128, 130, 132, 143, 145, 154, 161, 236, 255, 261, 276, 279, 287, 304, 364, 430, 464, 513, 528, 541, 562, 665, 672, 680, 707, 718, 747, 760, 782, 828, 875, 892, 974, 984, 987, 1037, 1058, 1070, 1073, 1080, 1091, 1154, 1248, 1367, 1426, 1440, 1462, 1524, 1598, 1623, 1627, 1863, 1985, 2132, 2188, 2196, 2340, 2460, 2508, 2626, 2640, 2739, 2856, 3092, 3158, 3262, 3315, 3326, 3482, 3638, 3982, 4018, 4036, ...
4 1, 2, 3, 4, 6, 8, 10, 12, 16, 20, 28, 40, 60, 92, 96, 104, 140, 148, 156, 300, 356, 408, 596, 612, 692, 732, 756, 800, 952, 996, 1004, 1228, 1268, 2240, 2532, 3060, 3796, 3824, 3944, ...
5 1, 2, 3, 4, 6, 7, 8, 10, 11, 12, 13, 18, 24, 28, 47, 48, 49, 56, 57, 88, 90, 92, 108, 110, 116, 120, 127, 134, 141, 149, 161, 171, 181, 198, 202, 206, 236, 248, 288, 357, 384, 420, 458, 500, 530, 536, 619, 620, 694, 798, 897, 929, 981, 992, 1064, 1134, 1230, 1670, 1807, 2094, 2162, 2369, 2516, 2649, 2988, 3407, 3888, ...
6 1, 2, 3, 4, 5, 6, 7, 8, 18, 21, 22, 24, 29, 30, 42, 50, 62, 71, 86, 90, 94, 118, 124, 127, 129, 144, 154, 186, 192, 214, 271, 354, 360, 411, 480, 509, 558, 575, 663, 764, 814, 825, 874, 1028, 1049, 1050, 1102, 1113, 1131, 1158, 1376, 1464, 1468, 1535, 1622, 1782, 1834, 1924, 2096, 2176, 2409, 2464, 2816, 3013, 3438, 3453, 3663, ...
7 3, 5, 6, 8, 13, 18, 21, 28, 30, 34, 36, 46, 48, 50, 54, 55, 58, 63, 76, 84, 94, 105, 122, 131, 148, 149, 224, 280, 288, 296, 332, 352, 456, 528, 531, 581, 650, 654, 730, 740, 759, 1026, 1047, 1065, 1460, 1660, 1699, 1959, 2067, 2260, 2380, 2665, 2890, 3238, 4020, ...
8 1, 2, 3, 6, 9, 18, 30, 42, 78, 87, 114, 138, 189, 303, 318, 330, 408, 462, 504, 561, 1002, 1389, 1746, 1794, 2040, 2418, 2790, 3894, 4077, ...
9 1, 2, 4, 6, 10, 12, 16, 18, 20, 30, 32, 36, 54, 64, 66, 118, 138, 152, 182, 232, 264, 336, 340, 380, 414, 446, 492, 540, 624, 720, 762, 1066, 1094, 1098, 1170, 1230, 1254, 1320, 1428, 1546, 2018, 2574, 2724, 2804, 2920, 3074, 3316, 3646, ...
10 1, 2, 3, 4, 9, 10, 12, 14, 19, 23, 24, 36, 38, 39, 48, 62, 93, 106, 120, 134, 150, 196, 294, 317, 320, 385, 586, 597, 654, 738, 945, 1031, 1172, 1282, 1404, 1426, 1452, 1521, 1752, 1812, 1836, 1844, 1862, 2134, 2232, 2264, 2667, 3750, 3903, 3927, ...
11 2, 4, 5, 6, 8, 9, 10, 14, 15, 17, 18, 19, 20, 27, 36, 42, 45, 52, 60, 73, 91, 104, 139, 205, 234, 246, 318, 358, 388, 403, 458, 552, 810, 855, 878, 907, 1114, 1131, 1220, 1272, 1431, 1470, 1568, 1614, 1688, 1696, 1907, 2029, 2136, 2288, 2535, 2577, ...
12 1, 2, 3, 5, 10, 12, 19, 20, 21, 22, 56, 60, 63, 70, 80, 84, 92, 97, 109, 111, 123, 164, 189, 218, 276, 317, 353, 364, 386, 405, 456, 511, 636, 675, 701, 793, 945, 1090, 1268, 1272, 1971, 2088, 2368, 2482, 2893, 2966, 3290, ...
13 2, 3, 5, 6, 7, 8, 9, 12, 16, 22, 24, 28, 33, 34, 38, 78, 80, 102, 137, 140, 147, 224, 230, 283, 304, 341, 360, 372, 384, 418, 420, 436, 483, 568, 570, 594, 737, 744, 855, 883, 991, 1021, 1193, 1222, 1615, 1628, 1838, 2032, 2146, 2302, 2530, 2830, 2958, 3030, 3528, 3671, 3885, ...
14 1, 3, 4, 6, 7, 14, 19, 24, 31, 33, 35, 36, 41, 55, 60, 106, 114, 129, 152, 153, 172, 222, 265, 286, 400, 448, 560, 584, 864, 1006, 1335, 1363, 1520, 1536, 1659, 1862, 1925, 2332, 2458, 2687, 3381, 3512, 3870, 3976, ...
15 3, 4, 6, 7, 14, 24, 43, 54, 58, 73, 85, 93, 102, 184, 220, 221, 228, 232, 247, 291, 305, 486, 487, 505, 551, 552, 590, 1029, 1194, 1274, 1406, 1444, 1532, 1548, 1748, 1986, 2093, 2182, 2202, 2579, 2781, 3054, 3239, 3696, ...
16 2, 4, 6, 8, 10, 14, 20, 30, 46, 48, 52, 70, 74, 78, 150, 178, 204, 298, 306, 346, 366, 378, 400, 476, 498, 502, 614, 634, 1120, 1266, 1530, 1898, 1912, 1972, 2548, 2770, 3738, 3850, ...
17 1, 2, 3, 5, 7, 8, 11, 12, 14, 15, 34, 42, 46, 47, 48, 50, 71, 77, 94, 110, 114, 147, 154, 176, 228, 235, 258, 275, 338, 350, 419, 450, 480, 515, 589, 624, 666, 716, 724, 810, 815, 1232, 1490, 1934, 2106, 2391, 2732, 2904, 3462, 3912, 4053, ...
18 1, 2, 3, 6, 14, 17, 21, 24, 30, 33, 38, 45, 46, 72, 78, 114, 146, 168, 288, 414, 440, 448, 665, 792, 801, 816, 975, 1165, 1176, 1267, 1466, 1513, 1882, 1920, 1998, 2194, 2272, 2643, 2800, 2946, 3434, 3504, 3813, 3866, 3957, ...
19 2, 3, 4, 6, 19, 20, 31, 34, 47, 56, 59, 61, 70, 74, 91, 92, 96, 98, 107, 120, 145, 156, 168, 242, 276, 314, 326, 337, 387, 565, 602, 612, 892, 984, 1061, 1067, 1079, 1262, 1328, 2356, 3033, 3419, 3501, 3963, ...
20 1, 3, 4, 6, 8, 9, 10, 11, 17, 30, 98, 100, 110, 126, 154, 158, 160, 168, 178, 182, 228, 266, 270, 280, 340, 416, 480, 574, 774, 980, 1052, 1139, 1338, 1418, 1474, 1487, 1594, 1902, 2326, 3112, 3520, 3808, 3830, ...
21 2, 3, 5, 6, 8, 9, 10, 11, 14, 17, 26, 43, 64, 74, 81, 104, 192, 271, 321, 335, 348, 404, 437, 445, 516, 671, 694, 788, 1788, 1943, 2343, 2742, 3031, 3135, ...
22 2, 5, 6, 7, 10, 21, 25, 26, 69, 79, 86, 93, 100, 101, 154, 158, 161, 171, 202, 214, 294, 354, 359, 424, 454, 602, 687, 706, 744, 857, 1028, 1074, 1136, 1150, 1345, 1408, 1525, 1572, 1578, 1988, 2142, 2665, ...
23 2, 5, 8, 11, 15, 22, 26, 39, 42, 45, 54, 56, 132, 134, 145, 147, 196, 212, 218, 252, 343, 580, 662, 816, 820, 846, 1078, 1092, 1174, 1189, 1548, 1632, 2040, 2180, 2348, 2732, 3100, 3181, 4010, ...
24 1, 2, 3, 4, 5, 8, 14, 19, 22, 38, 45, 53, 54, 70, 71, 117, 140, 144, 169, 186, 192, 195, 196, 430, 653, 661, 744, 834, 855, 870, 927, 1128, 1158, 1390, 1516, 1555, 1617, 1844, 2022, 2060, 2208, 2812, 3153, 3952, ...
25 2, 4, 6, 12, 14, 24, 28, 44, 46, 54, 58, 60, 118, 124, 144, 192, 210, 250, 268, 310, 496, 532, 1258, 1494, 1944, 2050, 2498, 2728, 3324, 3418, 3646, 3862, 4014, ...
26 1, 2, 4, 7, 9, 18, 20, 22, 24, 30, 43, 69, 132, 140, 186, 200, 210, 218, 267, 347, 454, 495, 554, 585, 645, 694, 980, 1028, 1060, 1098, 1432, 1714, 1828, 3513, 3786, ...
27 2, 3, 12, 21, 24, 36, 87, 93, 171, 249, 276, 360, 480, 621, 732, 780, 1716, 3843, ...
28 1, 2, 3, 5, 6, 8, 17, 21, 38, 81, 91, 96, 102, 132, 148, 156, 240, 258, 260, 276, 457, 464, 465, 500, 506, 535, 684, 746, 838, 930, 982, 1015, 1189, 1296, 1335, 1345, 1390, 1423, 2062, 2723, 2893, 3078, ...
29 4, 5, 6, 7, 8, 14, 30, 32, 39, 45, 50, 76, 116, 151, 222, 357, 402, 462, 570, 588, 636, 671, 695, 844, 1498, 1650, 1770, 3175, 3195, 3312, 3538, 3719, ...
30 1, 2, 5, 9, 11, 12, 21, 36, 51, 64, 91, 163, 174, 195, 230, 278, 318, 342, 346, 424, 530, 569, 578, 795, 984, 1094, 1167, 1335, 1564, 1605, 1658, 1789, 2159, 2204, 2225, 3366, 3458, 3615, ...
31 3, 7, 12, 17, 24, 30, 31, 33, 40, 176, 218, 308, 404, 420, 630, 693, 890, 915, 922, 1475, 2122, 2185, 2487, 2541, 2907, 3387, 4055, ...
32 1, 6, 30, 85, 110, 120, 320, 1050, 1065, 1385, 2490, 3080, 3920, ...
33 1, 2, 3, 10, 16, 25, 28, 30, 35, 36, 45, 56, 76, 87, 110, 134, 135, 197, 200, 220, 228, 314, 324, 330, 396, 498, 583, 624, 725, 806, 940, 1145, 1240, 1644, 1750, 2171, 2268, 2675, 2781, 2790, 2808, 3581, ...
34 3, 6, 8, 10, 13, 20, 24, 56, 87, 154, 164, 196, 282, 363, 428, 652, 744, 780, 860, 902, 952, 1178, 1493, 1540, 1643, 1904, 2184, 2277, 2468, 2943, ...
35 2, 4, 6, 8, 18, 21, 22, 26, 42, 128, 154, 158, 170, 180, 184, 192, 254, 313, 450, 624, 737, 762, 798, 874, 912, 1002, 1006, 1098, 1234, 1297, 1418, 1714, 1926, 2325, 2343, 2368, 2998, 3567, 4064, ...
36 2, 4, 12, 62, 72, 96, 180, 240, 382, 514, 688, 732, 734, 962, 1048, 1088, 1232, 1408, 2088, 2176, 2248, 2724, 3180, ...

Last fiddled with by sweety439 on 2020-11-04 at 12:33
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Old 2020-11-08, 11:31   #4
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OEIS sequences:

#1 = Permutable prime (repunit prime excluded, since if repunit prime incuded, then there will be infinitely many permutable primes)
#2 = Circular prime (repunit prime excluded, since if repunit prime incuded, then there will be infinitely many circular primes)
#3 = Left-truncatable prime
#4 = Right-truncatable prime
#5 = Minimal prime
#6 = Two-sided prime

(there is conjectured to be infinitely repunit primes (weakly primes, full-reptend primes, unique primes) in any given base)

A = Largest such prime in base n (written in base 10)
B = Length of largest such prime in base n
C = Number of such primes in base n


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Old 2020-11-08, 11:52   #5
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Data for the minimal primes, the left-truncatable primes, and the right-truncatable primes in bases 2 to 128: https://github.com/xayahrainie4793/primes/tree/master

Data is currently not complete

"kernel n": data for minimal primes base n
"left n" data for unsolved families for the "minimal prime problem" (like Sierpinski problem and Riesel problem) base n
"ltp n" data for left-truncatable primes base n
"rtp n" data for right-truncatable primes base n
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Old 2020-11-08, 12:11   #7
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Wikipedia pages:

repunit

permutable prime

circular prime

minimal prime

truncatable prime

weakly prime

Last fiddled with by sweety439 on 2020-11-09 at 16:29
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Old 2020-11-08, 12:14   #8
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Prime glossary pages:

repunit

minimal prime

left-truncatable prime

right-truncatable prime

deletable prime

permutable prime

circular prime
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Old 2020-11-08, 12:21   #9
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#1 = Permutable prime (repunit prime excluded, since if repunit prime incuded, then there will be infinitely many permutable primes)
#2 = Circular prime (repunit prime excluded, since if repunit prime incuded, then there will be infinitely many circular primes)
#3 = Left-truncatable prime
#4 = Right-truncatable prime
#5 = Minimal prime
#6 = Two-sided prime

(there is conjectured to be infinitely repunit primes (weakly primes, full-reptend primes, unique primes) in any given base)

A = Largest such prime in base n (written in base 10)
B = Length of largest such prime in base n
C = Number of such primes in base n

1A bases 3 to 20

2A bases 3 to 6

3A bases 3 to 53 (with missing terms)

3B bases 2 to 53 (with missing terms)

3C bases 2 to 53 (with missing terms)

4A bases 3 to 100

4B bases 2 to 53

4C bases 2 to 100

5A bases 2 to 42 (with missing terms)

5B bases 2 to 16

5C bases 2 to 16

6A bases 3 to 64

6C bases 2 to 64
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Old 2020-11-23, 01:10   #10
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The bases such that all minimal primes are known are 2-16, 18, 20, 22-24, 30, 42 and possible 60

The bases such that all left truncatable primes are known are 2-29, 31-35, 37-39, 41, 43, 47, 49, 51, 53, 55, 59, 61, 65, 67, 71, 73, 79, 83, 89

The bases such that all right truncatable primes are known are 2-100 and possible higher bases
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Old 2020-11-23, 01:17   #11
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Puzzles:

* Found all left truncatable primes in base b, for 2<=b<=256
* Found all right truncatable primes in base b, for 2<=b<=256
* Found all minimal primes in base b, for 2<=b<=256

(we allow strong probable primes >2^(2^16) to all prime bases 2<=p<=256 in place of proven primes, if the probable prime is <2^(2^16), then we need to prove its primality)
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