20191130, 06:42  #34 
Nov 2016
2,819 Posts 

20191207, 08:39  #35  
Nov 2016
2,819 Posts 
Quote:
Result file attached. 

20191207, 08:42  #36 
Nov 2016
2,819 Posts 
Base 40:
S{Q}d (86*40^n+37)/3: currently at n=87437, no (probable) prime found 
20201018, 13:39  #37 
Nov 2016
2,819 Posts 
Unsolved families:
Base 17: F1{9}: (4105*17^n9)/16 Base 19: EE1{6}: (15964*19^n1)/3 Base 21: G{0}FK: 7056*21^n+335 Base 25: EF{O}: 366*25^n1 O{L}8: (4975*25^n111)/8 CM{1}: (7729*25^n1)/24 E{1}E: (8425*25^n+311)/24 EE{1}: (8737*25^n1)/24 6M{F}9: (34525*25^n53)/8 F{1}F1: (225625*25^n+8399)/24 Base 26: {A}6F: (1352*26^n497)/5 {I}GL: (12168*26^n1243)/25 Base 31: E8{U}P: 13733*31^n6 {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^n7)/10 {L}G: (217*31^n57)/10 {L}CE: (6727*31^n2867)/10 M{P}: (137*31^n5)/6 {P}I: (155*31^n47)/6 {R}1: (279*31^n269)/10 {R}8: (279*31^n199)/10 {U}P8K: 29791*31^n5498 
20201020, 12:35  #38 
Nov 2016
5403_{8} Posts 
Base 31:
ILE{L}: (179637*31^n7)/10 [need not to be searched if a smaller prime for the "IE{L}: (5727*31^n7)/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^n3777)/10 [need not to be searched if a smaller prime for the "{L}G: (217*31^n57)/10" family were found] {L}9IG: (208537*31^n116307)/10 [need not to be searched if a smaller prime for either the "{L}G: (217*31^n57)/10" family or the "{L}9G: (6727*31^n3777)/10" family were found] {L}SO: (6727*31^n+2193)/10 {L}IS: (6727*31^n867)/10 MI{O}L: (108624*31^n19)/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^n8069)/10 [need not to be searched if a smaller prime for the "{R}1: (279*31^n269)/10" family were found] SP{0}K: 27683*31^n+20 Last fiddled with by sweety439 on 20201020 at 12:35 
20201020, 12:48  #39 
Nov 2016
2,819 Posts 
Base 35:
6W{P}4: (288855*35^n739)/34 [need not to be searched if a smaller prime for the "W{P}4: (38955*35^n739)/34" family were found] F8{0}F9: 652925*35^n+534 {Y}PO: 1225*35^n326 FQ{F}I: (656215*35^n+87)/34 PX{0}ER: 1112300*35^n+517 Q{P}4: (31815*35^n739)/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 20201021 at 06:58 
20201020, 13:31  #40 
Nov 2016
2,819 Posts 
Base 25:
F{O}KO: 9375*25^n+524 FO{K}O: (56375*25^n+19)/6 LO{L}8: (109975*25^n111)/8 [need not to be searched if a smaller prime for the "O{L}8: (4975*25^n111)/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^n143)/17 {L}E6: (25725*35^n8861)/34 P0{P}G: (1042125*35^n331)/34 {Q}PEM: (557375*35^n28046)/17 RU{A}C: (580300*35^n+29)/17 W{P}4: (38955*35^n739)/34 {X}MLX: (1414875*35^n472463)/34 X{M}Y: (20020*35^n+193)/17 
20201020, 15:49  #41 
Nov 2016
2,819 Posts 
Base 27:
8{0}9A: 5832*27^n+253 999{G}: (88577*27^n8)/13 C{L}E: (8991*27^n203)/26 E{I}F8: (139239*27^n1192)/13 {F}9FM: (295245*27^n113557)/26 Base 48: A{0}SP: 23040*48^n+1369 C{e}Z: (28992*48^n275)/47 {K}IP: (46080*48^n4297)/47 a{0}1: 1728*48^n+1 eL{0}Z: 93168*48^n+35 jc{e}Z: (4960608*48^n275)/47 
20201020, 16:26  #42 
Nov 2016
2,819 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, 487, 4551 60, 1938, ? Last fiddled with by sweety439 on 20210117 at 23:06 
20201021, 16:06  #43 
Nov 2016
101100000011_{2} 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*37^220211 (= FY{a_22021}) 1008*37^208951 (= 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) primes) 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) primes) 2488*49^29737+1 (= 11c{0_29736}1) 774*49^18341+1 (= Fd{0_18340}1) 1394*49^526981 (= SL{m_52698}) 1706*49^163371 (= Yd{m_16337}) Last fiddled with by sweety439 on 20210117 at 23:04 
20201021, 17:15  #44 
Nov 2016
101100000011_{2} 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^n1: 260K, see http://www.noprimeleftbehind.net/cru...onjectures.htm Base 31: F{G}, (1*31^n+1)/2: 2^192, see http://www.fermatquotient.com/PrimSerien/GenFermOdd.txt Base 32: 4{0}1, 4*32^n+1: (2^337)/5, see http://www.prothsearch.com/fermat.html G{0}1, 16*32^n+1: (2^349)/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: 2^242, 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: 2^242, see http://www.primegrid.com/stats_genefer.php Last fiddled with by sweety439 on 20210117 at 08:27 
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