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2019-11-30, 06:42   #34
sweety439

Nov 2016

1001110000002 Posts

Quote:
 Originally Posted by sweety439 A (probable) prime was found: (13998*40^12381+29)/13 Written in base 40, this number is Qa{U12380}X This number is likely the second-largest "base 40 minimal prime"
Another probable prime is (13998*40^13474+29)/13, but this is not minimal prime in base 40

2019-12-07, 08:39   #35
sweety439

Nov 2016

1001110000002 Posts

Quote:
 Originally Posted by sweety439 Base 36: O{L}Z (4428*36^n+67)/5: tested to n=50K, no (probable) prime found {P}SZ (6480*36^n+821)/7: currently at n=41566, no (probable) prime found Base 40: S{Q}d (86*40^n+37)/3: currently at n=59777, no (probable) prime found
Base 36 {P}SZ (6480*36^n+821)/7 tested to n=50K, no (probable) prime found.

Result file attached.
Attached Files
 base 36 {P}SZ family 8K-50K status.txt (271.6 KB, 64 views)

 2019-12-07, 08:42 #36 sweety439     Nov 2016 1001110000002 Posts Base 40: S{Q}d (86*40^n+37)/3: currently at n=87437, no (probable) prime found
 2020-10-18, 13:39 #37 sweety439     Nov 2016 249610 Posts Unsolved families: Base 17: F1{9}: (4105*17^n-9)/16 Base 19: EE1{6}: (15964*19^n-1)/3 Base 21: G{0}FK: 7056*21^n+335 Base 25: EF{O}: 366*25^n-1 O{L}8: (4975*25^n-111)/8 CM{1}: (7729*25^n-1)/24 E{1}E: (8425*25^n+311)/24 EE{1}: (8737*25^n-1)/24 6M{F}9: (34525*25^n-53)/8 F{1}F1: (225625*25^n+8399)/24 Base 26: {A}6F: (1352*26^n-497)/5 {I}GL: (12168*26^n-1243)/25 Base 31: E8{U}P: 13733*31^n-6 {F}RA: (961*31^n+733)/2 {F}G: (31*31^n+1)/2 {F}KO: (961*31^n+327)/2 IE{L}: (5727*31^n-7)/10 {L}G: (217*31^n-57)/10 {L}CE: (6727*31^n-2867)/10 M{P}: (137*31^n-5)/6 {P}I: (155*31^n-47)/6 {R}1: (279*31^n-269)/10 {R}8: (279*31^n-199)/10 {U}P8K: 29791*31^n-5498
 2020-10-20, 12:35 #38 sweety439     Nov 2016 26×3×13 Posts Base 31: ILE{L}: (179637*31^n-7)/10 [need not to be searched if a smaller prime for the "IE{L}: (5727*31^n-7)/10" family were found] L{F}G: (1333*31^n+1)/2 [need not to be searched if a smaller prime for the "{F}G: (31*31^n+1)/2" family were found] L0{F}G: (40393*31^n+1)/2 [need not to be searched if a smaller prime for either the "{F}G: (31*31^n+1)/2" family or the "L{F}G: (1333*31^n+1)/2" family were found] {L}9G: (6727*31^n-3777)/10 [need not to be searched if a smaller prime for the "{L}G: (217*31^n-57)/10" family were found] {L}9IG: (208537*31^n-116307)/10 [need not to be searched if a smaller prime for either the "{L}G: (217*31^n-57)/10" family or the "{L}9G: (6727*31^n-3777)/10" family were found] {L}SO: (6727*31^n+2193)/10 {L}IS: (6727*31^n-867)/10 MI{O}L: (108624*31^n-19)/5 P{F}G: (1581*31^n+1)/2 [need not to be searched if a smaller prime for the "{F}G: (31*31^n+1)/2" family were found] PEO{0}Q: 758973*31^n+26 {R}1R: (8649*31^n-8069)/10 [need not to be searched if a smaller prime for the "{R}1: (279*31^n-269)/10" family were found] SP{0}K: 27683*31^n+20 Last fiddled with by sweety439 on 2020-10-20 at 12:35
 2020-10-20, 12:48 #39 sweety439     Nov 2016 26·3·13 Posts Base 35: 6W{P}4: (288855*35^n-739)/34 [need not to be searched if a smaller prime for the "W{P}4: (38955*35^n-739)/34" family were found] F8{0}F9: 652925*35^n+534 {Y}PO: 1225*35^n-326 FQ{F}I: (656215*35^n+87)/34 PX{0}ER: 1112300*35^n+517 Q{P}4: (31815*35^n-739)/34 RF{0}CPI: 41160000*35^n+15593 Base 36: O{L}Z: (30996*36^n+469)/35 {P}SZ: (6480*36^n+821)/7 Base 40: S{Q}d: (3440*40^n+37)/3 Last fiddled with by sweety439 on 2020-10-21 at 06:58
 2020-10-20, 13:31 #40 sweety439     Nov 2016 47008 Posts Base 25: F{O}KO: 9375*25^n+524 FO{K}O: (56375*25^n+19)/6 LO{L}8: (109975*25^n-111)/8 [need not to be searched if a smaller prime for the "O{L}8: (4975*25^n-111)/8" family were found] M{1}F1: (330625*25^n+8399)/24 M1{0}8: 13775*25^n+8 Base 28: O{A}F: (18424*28^n+125)/27 Base 35: LAA{E}6: (15520820*35^n-143)/17 {L}E6: (25725*35^n-8861)/34 P0{P}G: (1042125*35^n-331)/34 {Q}PEM: (557375*35^n-28046)/17 RU{A}C: (580300*35^n+29)/17 W{P}4: (38955*35^n-739)/34 {X}MLX: (1414875*35^n-472463)/34 X{M}Y: (20020*35^n+193)/17
 2020-10-20, 15:49 #41 sweety439     Nov 2016 26·3·13 Posts Base 27: 8{0}9A: 5832*27^n+253 999{G}: (88577*27^n-8)/13 C{L}E: (8991*27^n-203)/26 E{I}F8: (139239*27^n-1192)/13 {F}9FM: (295245*27^n-113557)/26 Base 48: A{0}SP: 23040*48^n+1369 C{e}Z: (28992*48^n-275)/47 {K}IP: (46080*48^n-4297)/47 a{0}1: 1728*48^n+1 eL{0}Z: 93168*48^n+35 jc{e}Z: (4960608*48^n-275)/47
 2020-10-20, 16:26 #42 sweety439     Nov 2016 1001110000002 Posts The "minimal prime problem" is solved only in bases 2~16, 18, 20, 22~24, 30, 42, and maybe 60 Code: b, length of largest minimal prime base b, number of minimal primes base b 2, 2, 2 3, 3, 3 4, 2, 3 5, 5, 8 6, 5, 7 7, 5, 9 8, 9, 15 9, 4, 12 10, 8, 26 11, 45, 152 12, 8, 17 13, 32021, 228 14, 86, 240 15, 107, 100 16, 3545, 483 18, 33, 50 20, 449, 651 22, 764, 1242 23, 800874, 6021 24, 100, 306 30, 1024, 220 42, 4551, 487 60, ?, ? (in theory, <2000 digits) Last fiddled with by sweety439 on 2020-10-21 at 06:58
 2020-10-21, 16:06 #43 sweety439     Nov 2016 249610 Posts Some minimal (probable) primes with bases 28<=b<=50 not shown in https://github.com/RaymondDevillers/primes: (and hence some unsolved families can be removed) Base 37: (families FY{a} and R8{a} can be removed) 590*37^22021-1 (= FY{a_22021}) 1008*37^20895-1 (= R8{a_20895}) Base 40: (family Qa{U}X can be removed) (13998*40^12381+29)/13 (= Qa{U_12380}X) Base 45: (families O{0}1 and AO{0}1 can be removed, and hence families O{0}1F1, O{0}ZZ1, unless they have small (probable) prime) 24*45^18522+1 (= O{0_18521}1) 474*45^44791+1 (= AO{0_44790}1) [this prime is not minimal prime] Base 49: (families 11c{0}1, Fd{0}1, SL{m} and Yd{m} can be removed, and hence families S6L{m}, YUUd{m}, YUd{m}, unless they have small (probable) prime) 2488*49^29737+1 (= 11c{0_29736}1) 774*49^18341+1 (= Fd{0_18340}1) 1394*49^52698-1 (= SL{m_52698}) 1706*49^16337-1 (= Yd{m_16337}) Last fiddled with by sweety439 on 2020-10-30 at 23:39
 2020-10-21, 17:15 #44 sweety439     Nov 2016 26·3·13 Posts Although the test limit of all families in https://github.com/RaymondDevillers/primes are all 10K, but some families are in fact already tested to much higher.... Base 25: EF{O}, 366*25^n-1: 260K, see http://www.noprimeleftbehind.net/cru...onjectures.htm Base 31: F{G}, (1*31^n+1)/2: 2^19-2, see http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt Base 32: 4{0}1, 4*32^n+1: (2^33-12)/5, see http://www.prothsearch.com/fermat.html G{0}1, 16*32^n+1: (2^34-14)/5, see http://www.prothsearch.com/fermat.html UG{0}1, 976*32^n+1: 560K, see http://www.prothsearch.com/riesel1.html Base 38: 1{0}1 1*38^n+1: 2^24-2, see http://www.primegrid.com/stats_genefer.php Base 45: 9W1{0}1 19666*45^n+1: 100K, see http://www.noprimeleftbehind.net/cru...onjectures.htm Base 46: d4{0}1, 1798*46^n+1: 500K, see http://www.noprimeleftbehind.net/cru...onjectures.htm Base 48: a{0}1, 36*48^n+1: 500K, see http://www.noprimeleftbehind.net/cru...onjectures.htm Base 50: 1{0}1 1*50^n+1: 2^24-2, see http://www.primegrid.com/stats_genefer.php Last fiddled with by sweety439 on 2020-10-30 at 23:35

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