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Old 2020-11-15, 10:51   #12
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

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https://oeis.org/wiki/User:Charles_R...special_primes (List and expected numbers of many types of primes)

Last fiddled with by sweety439 on 2021-07-30 at 07:14
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Old 2020-11-15, 10:56   #13
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

24×191 Posts
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Quote:
Originally Posted by sweety439 View Post
My GitSub website for status for generalized (minimal primes, left truncatable primes, right truncatable primes in bases 2<=b<=160:

https://github.com/xayahrainie4793/primes (currently not complete and continue updating ....)
* Minimal prime

** 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, ?, ?, ?, ?, ?, ?

** 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, ?, ?, ?, ?, ?, ?

** 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), (≥81995)

** 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

* Left-truncatable prime

** 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, ?

** 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, ?

** 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)

** 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)

* Right-truncatable prime

** 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

** 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

** 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

** 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

Last fiddled with by sweety439 on 2021-06-02 at 06:17
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Old 2020-11-27, 05:07   #15
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

24·191 Posts
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Links for repunit:

https://stdkmd.net/nrr/repunit/
http://www.kurtbeschorner.de/
https://maths-people.anu.edu.au/~brent/factors.html
https://gmplib.org/~tege/repunit.html
https://repunit-koide.jimdo.com/
http://www.h4.dion.ne.jp/~rep/ (broken link: from wayback machine cached copy)
http://repunit:1031@repunits.skoberne.net/list/ (broken link: from wayback machine cached copy)

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Old 2020-11-27, 05:27   #18
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

24×191 Posts
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Prime programs:

PARI/GP
PRIMO
PFGW
LLR
SRSIEVE (broken link: from wayback machine cached copy, new link to download: SRSIEVE, SR1SIEVE, SR2SIEVE, PFGW, LLR and SRBSIEVE, also the BOINC Confederation for srsieve, sr1sieve, sr2sieve, srbsieve)
CKSIEVE
MTSIEVE
NewPGen
Proth
PrimeForm (broken link: from wayback machine cached copy)

(the PRIMO, PFGW and LLR zipped files are too large to be attached here)
Attached Files
File Type: 7z SRSIEVE.7z (157.5 KB, 31 views)
File Type: 7z CKSIEVE.7z (58.6 KB, 29 views)
File Type: zip newpgen.zip (74.3 KB, 18 views)
File Type: zip proth.zip (181.0 KB, 19 views)

Last fiddled with by sweety439 on 2021-09-20 at 18:26
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Old 2020-11-27, 05:44   #20
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

24×191 Posts
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Links for Aliquot sequence:

http://www.aliquot.de/aliquote.htm
http://christophe.clavier.free.fr/Al...e/Aliquot.html
http://www.aliquotes.com/
http://amicable.homepage.dk/tables.htm (broken link: from wayback machine cached copy)
http://62.198.248.44/aliquot/tables.htm
https://www.rechenkraft.net/aliquot/AllSeq.html
https://www.rieselprime.de/Others/Aliquot000.htm
https://members.loria.fr/PZimmermann...s/aliquot.html
http://christophe.clavier.free.fr/Al...e/Aliquot.html
https://www.math.ru.nl/~bosma/Projects/ali.html
http://djm.cc/amicable.html
http://djm.cc/aliquot-database/aliquot-database.uhtml
http://djm.cc/amicable.txt
http://djm.cc/amicable2.txt
http://djm.cc/sociable.txt
http://www.aliquotes.com/aliquotes_p..._entieres.html
https://oeis.org/history/view?seq=A333246&v=82 (now this sequence is known up to a(2703), see text file b333246)
http://factordb.com/sequences.php
http://www.aliquot.de/aliquote.htm
http://www.aliquot.de/lehmer.htm
http://www.aliquot.de/tabellen/aliquotg.htm
https://www.unirioja.es/cu/jvarona/table.html
http://www.aliquot.de/tabellen/tables.htm
http://www.numberphile.com/videos/220_284.html (broken link: from wayback machine cached copy this video in YouTube)
https://www.youtube.com/watch?v=R2eQVqdUQLI
http://www.aliquotes.com/remonter_suite_envers.html
http://www.aliquotes.com/autres_proc...iteratifs.html
http://www.cs.uleth.ca/~hadi/2016-09..._sequences.pdf
http://www.expmath.org/expmath/volum...0finishes1.pdf (broken link: from wayback machine pdf file attached below)
http://www.lafn.org/~ax810/analysis.htm (broken link: from wayback machine cached copy)
http://mklasson.com/aliquot.php
Attached Files
File Type: pdf 3630finishes1.pdf (163.4 KB, 42 views)
File Type: txt b333246.txt (238.8 KB, 41 views)

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Old 2020-11-27, 13:30   #21
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Apr 2019

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For prime gaps

https://github.com/primegap-list-project/prime-gap-list
Records can be automatically submitted at http://primegaps.cloudygo.com/
Data and graphs at https://primegap-list-project.github.io/lists/
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Old 2020-12-01, 19:32   #22
sweety439
 
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

305610 Posts
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Links for generalized Wieferich / generalized Wall-Sun-Sun primes:

http://www.fermatquotient.com/Fermat...FermQ_Sort.txt
http://www.fermatquotient.com/Fermat...FermQ_Sorg.txt
http://www.fermatquotient.com/Fermat...n/FermatQ3.txt
http://www.fermatquotient.com/Fermat...witchFermQ.txt
http://www.fermatquotient.com/Fermat...tient_Sort.txt
http://www1.uni-hamburg.de/RRZ/W.Kel...tQuotient.html (broken link: from wayback machine cached copy)
http://download2.polytechnic.edu.na/...ults/table.txt (broken link and both wayback machine and archive today did not achieve)
http://www.asahi-net.or.jp/~KC2H-MSM...11/fer_quo.htm
http://go.helms-net.de/math/expdioph...tory/index.htm
http://go.helms-net.de/math/expdioph...tquotients.pdf
http://go.helms-net.de/math/expdioph...ge2_table1.htm
https://members.loria.fr/PZimmermann...eferich.status
https://www.ams.org/journals/mcom/20...04-01666-7.pdf
https://www.cs.uleth.ca/~akbary/Akbary-Siavashi-I.pdf
https://www.maa.org/sites/default/fi...f.bannered.pdf
https://core.ac.uk/download/pdf/230075348.pdf
https://hal.archives-ouvertes.fr/hal-01062305/document
https://www.tapatalk.com/groups/doze...ites-t737.html
https://www.researchgate.net/publica...version_finale
http://www.cecm.sfu.ca/~mjm/WieferichBarker/ (broken link, new link: http://wayback.cecm.sfu.ca/~mjm/WieferichBarker/)
http://www.bitman.name/math/article/1321
https://www.primegrid.com/forum_thread.php?id=5098
http://www.hamiel.de/cgi-bin/sbb.cgi...forum=6&show=1
http://home.earthlink.net/~oddperfec...Quotients.html (broken link: from wayback machine cached copy)

https://www.uni-math.gwdg.de/jahnel/...ts/Fibams4.pdf
https://arxiv.org/pdf/1902.04795.pdf
https://www.fq.math.ca/Papers1/58-5/bouazzaoui.pdf

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