Type of primes in various bases

sweety439 · 2020-11-03, 09:06

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

sweety439 · 2020-11-03, 09:26

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)

sweety439 · 2020-11-03, 09:29

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, ...

sweety439 · 2020-11-08, 11:31

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

Code:

        A         B         C
#1   A317689   A??????   A??????
#2   A293142   A??????   A??????
#3   A103443   A103463   A076623
#4   A023107   A103483   A076586
#5   A326609   A330049   A330048
#6   A323137   A??????   A323390

sweety439 · 2020-11-08, 11:52

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

sweety439 · 2020-11-08, 11:55

left-truncatable primes for bases up to 120

right-truncatable primes for bases up to 90

minimal primes for bases up to 50

sweety439 · 2020-11-08, 12:11

Wikipedia pages:

repunit

permutable prime

circular prime

minimal prime

truncatable prime

weakly prime

sweety439 · 2020-11-08, 12:14

Prime glossary pages:

repunit

minimal prime

left-truncatable prime

right-truncatable prime

deletable prime

permutable prime

circular prime

sweety439 · 2020-11-08, 12:21

#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

sweety439 · 2020-11-23, 01:10

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

sweety439 · 2020-11-23, 01:17

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)

2020-11-08, 12:11	#7
sweety439 Nov 2016 2²·691 Posts	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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2020-11-03, 09:06	#1
sweety439 Nov 2016 2²×691 Posts	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, 13^320208+183, 105424857819287798806418819113233738918727566030978473259776662287591943095417282958456246916612161, 436635814641280043127962407363407208906111673434962498607709751248805460292422544779495998033626489944124062146459306989397233, 16^35449+145, ?, 249069897374447078426903207266791381270529, ?, (20^44916-2809)/19, ?, 22^76320+7041, (23^800873106-7)/11, 973767003942195520947294504280890002680537875404412883659428819153939518991719953852457999342229586282557076411687300474817686178175693329, ?, ?, ?, ?, ?, 30^102312+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

2020-11-03, 09:26	#2
sweety439 Nov 2016 ACC₁₆ Posts	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

2020-11-08, 11:31	#4
sweety439 Nov 2016 101011001100₂ Posts	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 Code: A B C #1 A317689 A?????? A?????? #2 A293142 A?????? A?????? #3 A103443 A103463 A076623 #4 A023107 A103483 A076586 #5 A326609 A330049 A330048 #6 A323137 A?????? A323390 Last fiddled with by sweety439 on 2020-11-08 at 11:31

2020-11-08, 11:52	#5
sweety439 Nov 2016 2²·691 Posts	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

2020-11-08, 11:55	#6
sweety439 Nov 2016 2²·691 Posts	left-truncatable primes for bases up to 120 right-truncatable primes for bases up to 90 minimal primes for bases up to 50

2020-11-08, 12:14	#8
sweety439 Nov 2016 2²×691 Posts	Prime glossary pages: repunit minimal prime left-truncatable prime right-truncatable prime deletable prime permutable prime circular prime

2020-11-08, 12:21	#9
sweety439 Nov 2016 2²·691 Posts	#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

2020-11-23, 01:10	#10
sweety439 Nov 2016 2²×691 Posts	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

2020-11-23, 01:17	#11
sweety439 Nov 2016 2²·691 Posts	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)