generalized minimal (probable) primes - Page 7

sweety439 · 2020-11-26, 04:36

Quote:

Originally Posted by sweety439

14:{0}:x:49

Code:

1,24253982091278071092686802139899494400000000000000000000000000000000000000000109
2,1009
3,1069
4,1129
5,3024349
6,1249
8,50929
9,1429
10,1489
11,1549
12,1609
13,1669
15,1789
16,5361922889755312850308759177923802244504459923744908273254400000000000000000000000000000000000000000000000000000000000000000000001009
17,3025069
18,3025129
19,2029
20,2089
22,51769
23,2269
24,10886401489
25,2389
26,52009
27,52069
29,52189
30,2689
31,2749
32,52369
33,181442029
34,52489
36,3049
37,3109
38,3169
39,3229
40,39191040002449
41,3026509
43,3469
44,3529
45,53149
46,181442809
47,3709
48,3769
50,3889
51,181443109
52,53569
53,53629
54,4129
55,(trivial factor of 59)
57,3027469
58,307117308965289984000000000000000003529
59,10886403589

21:{0}:x:49

Code:

1,75709
2,1429
3,1489
4,1549
5,1609
6,1669
8,1789
9,211631616000000589
10,76249
11,272160709
12,2029
13,2089
15,16329600949
16,2269
17,4537069
18,2389
19,4537189
20,272161249
22,12697896960000001369
23,2689
24,2749
25,2753361057228796079119709444688918393883353351941059461389077445343240031237662127438976850813717433212648483052318436843042263067280107067121663921269045680514764091347878987046902409665972186282803753885626203381672952078169757610858708358660096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001549
26,3527193600001609
27,77269
29,3049
30,3109
31,3169
32,3229
33,272162029
34,77689
36,3469
37,3529
38,77929
39,16329602389
40,3709
41,3769
43,3889
44,272162689
45,4538749
46,278553138848124030953717760000000000000000000000000002809
47,4129
48,(trivial factor of 59)
50,78649
51,12697896960000003109
52,4539169
53,979776003229
54,4549
55,58786560003349
57,4729
58,4789
59,592433080565760000000000003589

28:{0}:x:49

Code:

1,1789
2,789910774087680000000000000169
3,21772800229
4,101089
5,2029
6,2089
8,21772800529
9,2269
10,101449
11,2389
12,6048769
13,6048829
15,101749
16,2689
17,2749
18,101929
19,47394646445260800000000000001189
20,362881249
22,3049
23,3109
24,3169
25,3229
26,102409
27,78382080001669
29,3469
30,3529
31,80223303988259720914670714880000000000000000000000000000001909
32,102769
33,3709
34,3769
36,3889
37,103069
38,282175488000002329
39,6050389
40,4129
41,(trivial factor of 59)
43,1306368002629
44,2316350688374295151333383964863082569625926687057800374045900800000000000000000000000000000000000000000000000000000000000000000000000002689
45,103549
46,362882809
47,4549
48,21772802929
50,4729
51,4789
52,103969
53,4909
54,4969
55,104149
57,1039694019687845983054132464844800000000000000000000000000000000003469
58,5209
59,78382080003589

35:{0}:x:49

Code:

1,7560109
2,2269
3,126229
4,2389
5,126349
6,16456474460160000000000000409
8,453600529
9,2689
10,2749
11,5878656000000709
12,76187381760000000000769
13,97977600000829
15,3049
16,3109
17,3169
18,3229
19,127189
20,127249
22,3469
23,3529
24,27855313884812403095371776000000000000000000000000000001489
25,127549
26,3709
27,3769
29,3889
30,127849
31,7561909
32,7561969
33,4129
34,(trivial factor of 59)
36,453602209
37,1632960002269
38,7562329
39,128389
40,4549
41,128509
43,4729
44,4789
45,128749
46,4909
47,4969
48,352719360000002929
50,129049
51,5209
52,129169
53,129229
54,129289
55,5449
57,5569
58,129529
59,5689

42:{0}:x:49

Code:

1,9072109
2,2689
3,2749
4,32659200289
5,151549
6,151609
8,3049
9,3109
10,3169
11,3229
12,151969
13,152029
15,3469
16,3529
17,117573120001069
18,5614347706314368308492315310161920000000000000000000000000000000000001129
19,3709
20,3769
22,3889
23,152629
24,9073489
25,16850366041100048016273224228350264013299690448515611349014072815152914037687200443877077133470937907200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001549
26,4129
27,(trivial factor of 59)
29,152989
30,5485491486720000000001849
31,32659201909
32,544321969
33,4549
34,9074089
36,4729
37,4789
38,153529
39,4909
40,4969
41,117573120002509
43,20686430901833768712610953618533187671699305261361528832000000000000000000000000000000000000000000000000000000000000000002629
44,5209
45,153949
46,544322809
47,544322869
48,5449
50,5569
51,387215843042271258003015621585831529981559389785592810438298620409934449687415027238102244809934838667668586191368584982641890866197562403890778944989683725107200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003109
52,5689
53,5749
54,32659203289
55,5869
57,154669
58,1959552003529
59,154789

49:{0}:x:49

Code:

1,3049
2,3109
3,3169
4,3229
5,3379480093071544116029035238523182050306352376786936240751182230865067894959768623789993478122963368981956666059054838206787747840000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000349
6,176809
8,3469
9,3529
10,10584649
11,177109
12,3709
13,3769
15,3889
16,177409
17,137168640001069
18,140390781979454511600673751040000000000000000000000000000001129
19,4129
20,(trivial factor of 59)
22,635041369
23,38102401429
24,177889
25,177949
26,4549
27,178069
29,4729
30,4789
31,10585909
32,4909
33,4969
34,178489
36,178609
37,5209
38,635042329
39,1382343854653440000000000002389
40,10586449
41,5449
43,5569
44,179089
45,5689
46,5749
47,179269
48,5869
50,137168640003049
51,29628426240000003109
52,106662334464000000003169
53,635043229
54,6229
55,179749
57,10587469
58,6469
59,6529

Other possible such simple families: (since x:0:(69-x):49 has trivial factor of 59)

x:{0}:(69-x):(69-x):49

Code:

14,3225349
21,176989
28,47394646445260800000000000150109
35,250489
42,32659298869
49,402236156424545502745212987027034204727486491193140838400000000000000000000000000000000000000000000000000000000000000073249

sweety439 · 2020-11-26, 04:41

There are still these families:

* x:{0}:(69-x):y:49 (both x and y are divisible by 7)
* x:{0}:y:(69-x):49 (both x and y are divisible by 7)
* 46:46:{42}:49
* x:46:{42}:49 (x is divisible by 7)
* 46:x:{42}:49 (x is divisible by 7)

sweety439 · 2020-11-26, 16:20

Update the sieve files for the "minimal primes problem" in base 36

sweety439 · 2020-11-28, 18:59

Quote:

Originally Posted by sweety439

There are still these families:

* x:{0}:(69-x):y:49 (both x and y are divisible by 7)
* x:{0}:y:(69-x):49 (both x and y are divisible by 7)
* 46:46:{42}:49
* x:46:{42}:49 (x is divisible by 7)
* 46:x:{42}:49 (x is divisible by 7)

Simple family 46:46:{42}:49 has prime 168409

For the family x:46:{42}:49 (x is divisible by 7):

Code:

14,3192169
21,47407121744705084745769
28,17401277249084745769
35,100156988745769
42,9240169
49,179209

For the family 46:x:{42}:49 (x is divisible by 7):

Code:

14,599337769
21,166909
28,167329
35,10064569
42,(trivial factor of 53, same as 46:{42}:49
49,7865395004745769

sweety439 · 2020-11-29, 08:18

Quote:

Originally Posted by sweety439

Other possible such simple families: (since x:0:(69-x):49 has trivial factor of 59)

x:{0}:(69-x):(69-x):49

Code:

14,3225349
21,176989
28,47394646445260800000000000150109
35,250489
42,32659298869
49,402236156424545502745212987027034204727486491193140838400000000000000000000000000000000000000000000000000000000000000073249

The corresponding number should contain x:{0}:(69-x):(69-x):49, thus the exponent n of x*60^n+(69-x)*3600+(69-x)*60+49 must be >=3

thus the numbers should be:

Code:

14,3225349
21,34864577508285536715621843874728423450542982178891555528152012131493522929364204109502946145026849325046917080053260518080831302972748957603118253490089245371424805240428862727380360124313862377115462690866801581738795217778114560000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000175729
28,47394646445260800000000000150109
35,7684489
42,32659298869
49,402236156424545502745212987027034204727486491193140838400000000000000000000000000000000000000000000000000000000000000073249

sweety439 · 2020-11-29, 08:33

Quote:

Originally Posted by sweety439

x:{14}:49

Code:

1,109
2,8089
3,229
4,15289
5,349
6,409
8,1779289
9,33289
10,132675289
11,709
12,769
13,829
15,20055578263423416146440677966101694915289
16,1009
17,1069
18,1129
19,249315289
20,1249
22,1037502915289
23,1429
24,1489
25,1549
26,1609
27,1669
29,1789
30,6531289
31,6747289
32,116089
33,2029
34,2089
36,130489
37,2269
38,495555289
39,2389
40,144889
41,103182884390444449640082580739273165590541602171762902235022709553359196234458364272060077833460415740804281702234241751684562368942580406237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915289
43,155689
44,2689
45,2749
46,465965333694915289
47,10203289
48,37509315289
50,3049
51,3109
52,3169
53,3229
54,702915289
55,11931289
57,3469
58,3529
59,213289

x:{21}:49

Code:

1,109
2,508909
3,229
4,56452909
5,349
6,409
8,30109
9,94286240542372909
10,37309
11,709
12,769
13,829
15,42986782372909
16,1009
17,1069
18,1129
19,69709
20,1249
22,4025817357839737065999049857469767607759032979106716427631968228584180718644067796610169491525423728813559322033898305084745762711864406779661016949152542372909
23,1429
24,1489
25,1549
26,1609
27,1669
29,1789
30,66078257013152542372909
31,112909
32,6988909
33,2029
34,2089
36,101773342372909
37,2269
38,497092909
39,2389
40,31380772909
41,535972909
43,156109
44,2689
45,2749
46,166909
47,170509
48,10444909
50,3049
51,3109
52,3169
53,3229
54,195709
55,717412909
57,3469
58,3529
59,12820909

x:{28}:49

Code:

1,109
2,8929
3,229
4,57990529
5,349
6,409
8,30529
9,34129
10,2262529
11,709
12,769
13,829
15,3342529
16,1009
17,1069
18,1129
19,4206529
20,1249
22,80929
23,1429
24,1489
25,1549
26,1609
27,1669
29,1789
30,394950529
31,113329
32,116929
33,2029
34,2089
36,472710529
37,2269
38,8310529
39,2389
40,8742529
41,4212156168942609355932203389830529
43,9390529
44,2689
45,2749
46,167329
47,1041447436333870756881355932203389830529
48,13781461655186262022942372881355932203389830529
50,3049
51,3109
52,3169
53,3229
54,331946136337921041355932203389830529
55,199729
57,3469
58,3529
59,214129

x:{35}:49

Code:

1,109
2,9349
3,229
4,771484637288149
5,349
6,409
8,30949
9,34549
10,38149
11,709
12,769
13,829
15,56149
16,1009
17,1069
18,1129
19,70549
20,1249
22,81349
23,1429
24,1489
25,1549
26,1609
27,1669
29,1789
30,6608149
31,113749
32,25344488149
33,2029
34,2089
36,131749
37,2269
38,23335844534237288149
39,2389
40,526088149
41,149749
43,33898088149
44,2689
45,2749
46,10064149
47,185120325561205169675135454687984165581220276782105983361193164168670838265752820260904448577571678108045870876576322502449572547744055070802594515527926156691477915758601548938853501303980626387044701079429027352148995318212751455646534728345092572787387347410490834215458172781888350653835992601161966471095319325576754886993561238893441826145675686736477047030489460058140333352185261905102459753937730302319495540099005728377120233422356413887591971257315898743429492383226804915072909057608763313496683212160248130680520291356694770983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288149
48,10496149
50,3049
51,3109
52,3169
53,3229
54,196549
55,12008149
57,3469
58,3529
59,12872149

x:{42}:49

Code:

1,109
2,9769
3,229
4,170945053505084745769
5,349
6,409
8,1881769
9,2097769
10,38569
11,709
12,769
13,829
15,56569
16,1009
17,1069
18,1129
19,70969
20,1249
22,81769
23,1429
24,1489
25,1549
26,1609
27,1669
29,1789
30,110569
31,6849769
32,7065769
33,2029
34,2089
36,132169
37,2269
38,139369
39,2389
40,31657545769
41,150169
43,33990345769
44,2689
45,2749
46,(trivial factor of 53)
47,10305769
48,1767252099905084745769
50,3049
51,3109
52,3169
53,3229
54,11817769
55,200569
57,3469
58,3529
59,12897769

{14}:x:49

Code:

1,3074509
2,31719478566747843550804041300349830508474576271186440677966101694914569
3,11070914629
4,11070914689
5,184514749
6,11070914809
8,50929
9,50989
10,3075049
11,51109
12,51169
13,51229
15,51349
16,3075409
17,8608743701694915469
18,516524622101694915529
19,11070915589
20,184515649
22,51769
23,51829
24,664254915889
25,51949
26,52009
27,52069
29,52189
30,52249
31,39855294916309
32,52369
33,3076429
34,52489
36,52609
37,664254916669
38,30991477326101694916729
39,3076789
40,11070916849
41,664254916909
43,184517029
44,53089
45,53149
46,53690481146394350663097813232332427347712798372881355932203389830508474576271186440677966101694917209
47,53269
48,664254917329
50,86756301967596040677966101694917449
51,11070917509
52,53569
53,53629
54,3077689
55,3147493094329085095522234576271186440677966101694917749
57,30991477326101694917869
58,184517929
59,39855294917989

{21}:x:49

Code:

1,75709
2,10041238653656949152542371769
3,4611829
4,276771889
5,16606371949
6,4612009
8,76129
9,616626663337578078627630562878800705084745762711864406779661016949152542372189
10,76249
11,645936492161087054050399981653446997706215532953486454915466633416169490161247457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372309
12,76369
13,996382372429
15,4612549
16,4612609
17,4612669
18,276772729
19,4612789
20,4612849
22,4612969
23,77029
24,276773089
25,16606373149
26,4613209
27,77269
29,276773389
30,4613449
31,77509
32,77569
33,4613629
34,77689
36,16606373809
37,276773869
38,77929
39,16606373989
40,78049
41,4614109
43,78229
44,59782942374289
45,4614349
46,6071553036900241310806779661016949152542374409
47,276774469
48,61187265753757414256952240162711864406779661016949152542374529
50,78649
51,774786933152542374709
52,996382374769
53,4614829
54,78889
55,52209837304507200077039765027430616624964848906126524755206192493399488812789496523127382219681677062442951316647311186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542374949
57,4615069
58,996382375129
59,276775189

{28}:x:49

Code:

1,81583021005009885675936320216949152542372881355932203389828909
2,85460868854823834608016221386772928746969615932515587546395079909292691525423728813559322033898305084745762711864406779661016949152542372881355932203389828969
3,22141829029
4,101089
5,101149
6,101209
8,6149329
9,6149389
10,101449
11,286958123389829509
12,10410756236111524881355932203389829569
13,369029629
15,101749
16,79710589829809
17,101869
18,101929
19,1328509829989
20,6150049
22,13388318204875932203389830169
23,102229
24,6150289
25,79710589830349
26,102409
27,1328509830469
29,6150589
30,6150649
31,29828045081330194812832118462406904082062665762711864406779661016949152542372881355932203389830709
32,102769
33,102829
34,286958123389830889
36,41126317117261134141412615065804034201951786857394034478949601447152874939439946846072866224064662010793220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389831009
37,103069
38,6151129
39,1328509831189
40,369031249
41,369031309
43,286958123389831429
44,1328509831489
45,103549
46,1033049244203389831609
47,103669
48,6151729
50,1328509831849
51,286958123389831909
52,103969
53,37478722450001489572881355932203389832029
54,104089
55,104149
57,6152269
58,1328509832329
59,6152389

{35}:x:49

Code:

1,81475573154959817379255597463815552667176545024717505666213665960638224320021112459781503325113716943629003292963749951159320447728997238620350548107901686289125472897903137985503182233361374542375162900682265823294796999737443473337843435573308433456959404707058320810457306411455933006101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237286109
2,1660637286169
3,126229
4,17128518426043835517434182302188908474576271186440677966101694915254237286289
5,126349
6,36429318221401447864840677966101694915254237286409
8,77478693315254237286529
9,7686589
10,7686649
11,27677286709
12,99638237286769
13,461286829
15,126949
16,1660637287009
17,461287069
18,1660637287129
19,127189
20,127249
22,607155303690024131080677966101694915254237287369
23,131145545597045212313426440677966101694915254237287429
24,36429318221401447864840677966101694915254237287489
25,127549
26,127609
27,127669
29,27677287789
30,127849
31,358697654237287909
32,461287969
33,21521859254237288029
34,99638237288089
36,7688209
37,1660637288269
38,1660637288329
39,128389
40,128449
41,128509
43,128629
44,461288689
45,128749
46,7688809
47,358697654237288869
48,7688929
50,129049
51,7689109
52,129169
53,129229
54,129289
55,21521859254237289349
57,129469
58,129529
59,129589

{42}:x:49

Code:

1,9223309
2,293439587902707111288657562346647653394212382542384936694711075914089081641468094666645578615570550709924319586579296659981779875032195661701462202096102293874185480241052744144833349365537276799785969205297493379562404092952314178395004440542139367761173708310416661107311234222306240316209631923293822273260390016005704126405409242393725556515881932954120677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084743369
3,151429
4,260268905902788122033898305084743489
5,151549
6,151609
8,151729
9,95158435700243530652412123901049491525423728813559322033898305084743789
10,151849
11,151909
12,151969
13,152029
15,334707955121898305084744149
16,33212744209
17,9224269
18,25826231105084744329
19,152389
20,33212744449
22,1992764744569
23,152629
24,9224689
25,33212744749
26,152809
27,553544869
29,152989
30,1085381915311180600372601407525931962389847751970245597672814187895728453642389622010356871067432479240127281624918875843807895776453427504154910355073723811485480200485147288814532682450893550065346880581428503092670144866199408686377359578222051485037152838513072612496791202198960786455011981346714830632452284175840153078825137962409229301085120863398324900668527102405288924544210878811218940250587703349451751315140419049505572840115309385837985597640170169004994591035237463955094223324926699100962730596525138946332290428960176322975631221744617520009977331177155716098492037390962017969334604994823460496054237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745049
31,3452320032561365140374087785000799083572067796610169491525423728813559322033898305084745109
32,33212745169
33,1992764745229
34,9225289
36,153409
37,153469
38,153529
39,153589
40,153649
41,9225709
43,202385101230008043693559322033898305084745829
44,153889
45,153949
46,430437185084746009
47,9226069
48,1992764746129
50,553546249
51,33212746309
52,154369
53,1204948638438833898305084746429
54,95158435700243530652412123901049491525423728813559322033898305084746489
55,9226549
57,154669
58,33212746729
59,154789

x:{56}:49

Code:

1,109
2,232903489510723542345762711864406779661009
3,229
4,64141009
5,349
6,409
8,6958861009
9,35809
10,39409
11,709
12,769
13,829
15,2678845179661009
16,1009
17,1069
18,1129
19,71809
20,1249
22,82609
23,1429
24,1489
25,1549
26,1609
27,1669
29,1789
30,111409
31,24843661009
32,25621261009
33,2029
34,2089
36,6206038779661009
37,2269
38,2505535405903813370724804403593323757937224648962120170600421596767457627118644067796610169491525423728813559322033898305084745762711864406779661009
39,2389
40,147409
41,151009
43,158209
44,2689
45,2749
46,169009
47,1352698292914071864406779661009
48,3005939172097353755247425084745762711864406779661009
50,3049
51,3109
52,3169
53,3229
54,712141009
55,265108420301689108028745762711864406779661009
57,3469
58,3529
59,36248960086779661009

{56}:x:49

Code:

1,201709
2,201769
3,201829
4,201889
5,(unknown)--------------------------------------------
6,12118009
8,202129
9,9653019592485633973013465317098305084745762711864406779661016989
10,2620643796649
11,202309
12,566400676881355969
13,5709735191002302915254237288135629
15,202549
16,58945898613104908796787281723327929495504791864406779661016949152542372881355932203389830508474609
17,567254718915254269
18,202729
19,12165589
20,12169249
22,568108760949152569
23,12180229
24,2046421359945762711889
25,2047036270210169491549
26,203209
27,7093761567185965006603828947492636122315332510451660944126786645957854271249499254305367632322963084970458439570233744677754294570009344165309519479915483916060404477260724290563504102526168108734063115285915290869621533585153192590815828858408818278898724882400084482921884840835304669997229790232023533140916445257577809774331239487911472434979629754359717806594801121257152551530794852095579580308470842508145255117645170320709345089612366101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050869
29,122969754676067796610189
30,203449
31,1188311170943907960149478894148859142785502131611931784122256194336006619664718924985760162565866809427612081912641567081289109267479099879367407659887603855337724488646981970874823867396949529636127713094173227389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169491525423728813559322033898305084745762711864406779661016949152542372881355932203389830508474576271186440677966101694915254237288135593220338983050847457627118644067796610169509
32,203569
33,2638831728829
34,12220489
36,203809
37,203869
38,443886502387850847457627129
39,203989
40,12530020127900548285031371932203389830508474576271186449
41,12533767143489035291097469830508474576271186440677966109
43,44112325429
44,(unknown)--------------------------------------------
45,9533955905084749
46,12264409
47,445081887941857627118644069
48,2159152280280878917332772737414035022878368881841808054237288135593220338983050847457627118644067796610169491525423729
50,2652274983049
51,2063023937084745762709
52,44230942369
53,9781221482636363793361365248867796610169491525423728813559322029
54,44257301689
55,12297349
57,205069
58,205129
59,12311989

sweety439 · 2020-11-29, 08:45

Quote:

Originally Posted by sweety439

14:{0}:x:49

Code:

1,24253982091278071092686802139899494400000000000000000000000000000000000000000109
2,1009
3,1069
4,1129
5,3024349
6,1249
8,50929
9,1429
10,1489
11,1549
12,1609
13,1669
15,1789
16,5361922889755312850308759177923802244504459923744908273254400000000000000000000000000000000000000000000000000000000000000000000001009
17,3025069
18,3025129
19,2029
20,2089
22,51769
23,2269
24,10886401489
25,2389
26,52009
27,52069
29,52189
30,2689
31,2749
32,52369
33,181442029
34,52489
36,3049
37,3109
38,3169
39,3229
40,39191040002449
41,3026509
43,3469
44,3529
45,53149
46,181442809
47,3709
48,3769
50,3889
51,181443109
52,53569
53,53629
54,4129
55,(trivial factor of 59)
57,3027469
58,307117308965289984000000000000000003529
59,10886403589

21:{0}:x:49

Code:

1,75709
2,1429
3,1489
4,1549
5,1609
6,1669
8,1789
9,211631616000000589
10,76249
11,272160709
12,2029
13,2089
15,16329600949
16,2269
17,4537069
18,2389
19,4537189
20,272161249
22,12697896960000001369
23,2689
24,2749
25,2753361057228796079119709444688918393883353351941059461389077445343240031237662127438976850813717433212648483052318436843042263067280107067121663921269045680514764091347878987046902409665972186282803753885626203381672952078169757610858708358660096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001549
26,3527193600001609
27,77269
29,3049
30,3109
31,3169
32,3229
33,272162029
34,77689
36,3469
37,3529
38,77929
39,16329602389
40,3709
41,3769
43,3889
44,272162689
45,4538749
46,278553138848124030953717760000000000000000000000000002809
47,4129
48,(trivial factor of 59)
50,78649
51,12697896960000003109
52,4539169
53,979776003229
54,4549
55,58786560003349
57,4729
58,4789
59,592433080565760000000000003589

28:{0}:x:49

Code:

1,1789
2,789910774087680000000000000169
3,21772800229
4,101089
5,2029
6,2089
8,21772800529
9,2269
10,101449
11,2389
12,6048769
13,6048829
15,101749
16,2689
17,2749
18,101929
19,47394646445260800000000000001189
20,362881249
22,3049
23,3109
24,3169
25,3229
26,102409
27,78382080001669
29,3469
30,3529
31,80223303988259720914670714880000000000000000000000000000001909
32,102769
33,3709
34,3769
36,3889
37,103069
38,282175488000002329
39,6050389
40,4129
41,(trivial factor of 59)
43,1306368002629
44,2316350688374295151333383964863082569625926687057800374045900800000000000000000000000000000000000000000000000000000000000000000000000002689
45,103549
46,362882809
47,4549
48,21772802929
50,4729
51,4789
52,103969
53,4909
54,4969
55,104149
57,1039694019687845983054132464844800000000000000000000000000000000003469
58,5209
59,78382080003589

35:{0}:x:49

Code:

1,7560109
2,2269
3,126229
4,2389
5,126349
6,16456474460160000000000000409
8,453600529
9,2689
10,2749
11,5878656000000709
12,76187381760000000000769
13,97977600000829
15,3049
16,3109
17,3169
18,3229
19,127189
20,127249
22,3469
23,3529
24,27855313884812403095371776000000000000000000000000000001489
25,127549
26,3709
27,3769
29,3889
30,127849
31,7561909
32,7561969
33,4129
34,(trivial factor of 59)
36,453602209
37,1632960002269
38,7562329
39,128389
40,4549
41,128509
43,4729
44,4789
45,128749
46,4909
47,4969
48,352719360000002929
50,129049
51,5209
52,129169
53,129229
54,129289
55,5449
57,5569
58,129529
59,5689

42:{0}:x:49

Code:

1,9072109
2,2689
3,2749
4,32659200289
5,151549
6,151609
8,3049
9,3109
10,3169
11,3229
12,151969
13,152029
15,3469
16,3529
17,117573120001069
18,5614347706314368308492315310161920000000000000000000000000000000000001129
19,3709
20,3769
22,3889
23,152629
24,9073489
25,16850366041100048016273224228350264013299690448515611349014072815152914037687200443877077133470937907200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001549
26,4129
27,(trivial factor of 59)
29,152989
30,5485491486720000000001849
31,32659201909
32,544321969
33,4549
34,9074089
36,4729
37,4789
38,153529
39,4909
40,4969
41,117573120002509
43,20686430901833768712610953618533187671699305261361528832000000000000000000000000000000000000000000000000000000000000000002629
44,5209
45,153949
46,544322809
47,544322869
48,5449
50,5569
51,387215843042271258003015621585831529981559389785592810438298620409934449687415027238102244809934838667668586191368584982641890866197562403890778944989683725107200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003109
52,5689
53,5749
54,32659203289
55,5869
57,154669
58,1959552003529
59,154789

49:{0}:x:49

Code:

1,3049
2,3109
3,3169
4,3229
5,3379480093071544116029035238523182050306352376786936240751182230865067894959768623789993478122963368981956666059054838206787747840000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000349
6,176809
8,3469
9,3529
10,10584649
11,177109
12,3709
13,3769
15,3889
16,177409
17,137168640001069
18,140390781979454511600673751040000000000000000000000000000001129
19,4129
20,(trivial factor of 59)
22,635041369
23,38102401429
24,177889
25,177949
26,4549
27,178069
29,4729
30,4789
31,10585909
32,4909
33,4969
34,178489
36,178609
37,5209
38,635042329
39,1382343854653440000000000002389
40,10586449
41,5449
43,5569
44,179089
45,5689
46,5749
47,179269
48,5869
50,137168640003049
51,29628426240000003109
52,106662334464000000003169
53,635043229
54,6229
55,179749
57,10587469
58,6469
59,6529

the exponent n must be >=2

thus the numbers should be:

14:{0}:x:49

Code:

1,24253982091278071092686802139899494400000000000000000000000000000000000000000109
2,85310363601469440000000000000000169
3,181440229
4,181440289
5,3024349
6,3024409
8,50929
9,50989
10,3024649
11,51109
12,51169
13,51229
15,51349
16,5361922889755312850308759177923802244504459923744908273254400000000000000000000000000000000000000000000000000000000000000000000001009
17,3025069
18,3025129
19,10886401189
20,39191040001249
22,51769
23,51829
24,10886401489
25,51949
26,52009
27,52069
29,52189
30,52249
31,3025909
32,52369
33,181442029
34,52489
36,52609
37,181442269
38,3026329
39,3026389
40,39191040002449
41,3026509
43,30474952704000000002629
44,53089
45,53149
46,181442809
47,53269
48,3026929
50,8465264640000003049
51,181443109
52,53569
53,53629
54,519847009843922991527066232422400000000000000000000000000000000003289
55,(trivial factor of 59)
57,3027469
58,307117308965289984000000000000000003529
59,10886403589

21:{0}:x:49

Code:

1,75709
2,272160169
3,1658433468412565913600000000000000000000229
4,16329600289
5,82957725632529349183096088094078902389028226882976538255839640308244599894942626191769600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000349
6,761873817600000000409
8,76129
9,211631616000000589
10,76249
11,272160709
12,76369
13,979776000829
15,16329600949
16,58786560001009
17,4537069
18,272161129
19,4537189
20,272161249
22,12697896960000001369
23,77029
24,16329601489
25,2753361057228796079119709444688918393883353351941059461389077445343240031237662127438976850813717433212648483052318436843042263067280107067121663921269045680514764091347878987046902409665972186282803753885626203381672952078169757610858708358660096000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001549
26,3527193600001609
27,77269
29,1658433468412565913600000000000000000001789
30,2742745743360000000001849
31,77509
32,77569
33,272162029
34,77689
36,3527193600002209
37,12697896960000002269
38,77929
39,16329602389
40,78049
41,4538509
43,78229
44,272162689
45,4538749
46,278553138848124030953717760000000000000000000000000002809
47,2742745743360000000002869
48,(trivial factor of 59)
50,78649
51,12697896960000003109
52,4539169
53,979776003229
54,78889
55,58786560003349
57,16329603469
58,3527193600003529
59,592433080565760000000000003589

28:{0}:x:49

Code:

1,6048109
2,789910774087680000000000000169
3,21772800229
4,101089
5,101149
6,101209
8,21772800529
9,13165179568128000000000000589
10,101449
11,6048709
12,6048769
13,6048829
15,101749
16,21772801009
17,101869
18,101929
19,47394646445260800000000000001189
20,362881249
22,362881369
23,102229
24,6049489
25,21772801549
26,102409
27,78382080001669
29,21772801789
30,1306368001849
31,80223303988259720914670714880000000000000000000000000000001909
32,102769
33,102829
34,6050089
36,362882209
37,103069
38,282175488000002329
39,6050389
40,78382080002449
41,(trivial factor of 59)
43,1306368002629
44,2316350688374295151333383964863082569625926687057800374045900800000000000000000000000000000000000000000000000000000000000000000000000002689
45,103549
46,362882809
47,103669
48,21772802929
50,1306368003049
51,614234617930579968000000000000000003109
52,103969
53,78382080003229
54,104089
55,104149
57,1039694019687845983054132464844800000000000000000000000000000000003469
58,362883529
59,78382080003589

35:{0}:x:49

Code:

1,7560109
2,8295772563252934918309608809407890238902822688297653825583964030824459989494262619176960000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000169
3,126229
4,453600289
5,126349
6,16456474460160000000000000409
8,453600529
9,16456474460160000000000000589
10,1632960000649
11,5878656000000709
12,76187381760000000000769
13,97977600000829
15,126949
16,7561009
17,453601069
18,453601129
19,127189
20,127249
22,21163161600000001369
23,1058618139930670449693711081043149246240742123451547245555903649209833331097600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001429
24,27855313884812403095371776000000000000000000000000000001489
25,127549
26,127609
27,127669
29,7561789
30,127849
31,7561909
32,7561969
33,464255231413540051589529600000000000000000000000000002029
34,(trivial factor of 59)
36,453602209
37,1632960002269
38,7562329
39,128389
40,128449
41,128509
43,128629
44,5878656000002689
45,128749
46,7562809
47,7562869
48,352719360000002929
50,129049
51,1269789696000000003109
52,129169
53,129229
54,129289
55,1632960003349
57,129469
58,129529
59,129589

42:{0}:x:49

Code:

1,9072109
2,25395793920000000169
3,151429
4,32659200289
5,151549
6,151609
8,151729
9,9072589
10,151849
11,151909
12,151969
13,152029
15,9072949
16,32659201009
17,117573120001069
18,5614347706314368308492315310161920000000000000000000000000000000000001129
19,152389
20,9073249
22,9073369
23,152629
24,9073489
25,16850366041100048016273224228350264013299690448515611349014072815152914037687200443877077133470937907200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001549
26,152809
27,(trivial factor of 59)
29,152989
30,5485491486720000000001849
31,32659201909
32,544321969
33,5485491486720000000002029
34,9074089
36,153409
37,153469
38,153529
39,153589
40,153649
41,117573120002509
43,20686430901833768712610953618533187671699305261361528832000000000000000000000000000000000000000000000000000000000000000002629
44,153889
45,153949
46,544322809
47,544322869
48,9074929
50,9075049
51,387215843042271258003015621585831529981559389785592810438298620409934449687415027238102244809934838667668586191368584982641890866197562403890778944989683725107200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003109
52,154369
53,14772772476559131803121204930915190318100750753041978023597954641499975561510557076017704836828037656902825724306702668559522982093578013910983164901324528981969784421602291230795234581969764786884845389890123210865111407518668131288178601114344226068215563391858075723302927140211618251554048985252761126263361099239362046694128659460701378499098943318291633703276353429221375899179448599101811449547970964749313875828661985567305524048394452992000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003229
54,32659203289
55,25395793920000003349
57,154669
58,1959552003529
59,154789

49:{0}:x:49

Code:

1,176509
2,635040169
3,176629
4,23580260366520346895667724302680064000000000000000000000000000000000000000289
5,3379480093071544116029035238523182050306352376786936240751182230865067894959768623789993478122963368981956666059054838206787747840000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000349
6,176809
8,10584529
9,176989
10,10584649
11,177109
12,8230118400000769
13,8230118400000829
15,635040949
16,177409
17,137168640001069
18,140390781979454511600673751040000000000000000000000000000001129
19,177589
20,(trivial factor of 59)
22,635041369
23,38102401429
24,177889
25,177949
26,493807104000001609
27,178069
29,10585789
30,178249
31,10585909
32,10585969
33,383984404070400000000002029
34,178489
36,178609
37,10586269
38,635042329
39,1382343854653440000000000002389
40,10586449
41,178909
43,179029
44,179089
45,38102402749
46,179209
47,179269
48,38102402929
50,137168640003049
51,29628426240000003109
52,106662334464000000003169
53,635043229
54,179689
55,179749
57,10587469
58,635043529
59,179989

56:{0}:x:49

Code:

1,201709
2,201769
3,201829
4,201889
5,9405849600000349
6,73708154151669596160000000000000000000409
8,202129
9,12096589
10,2031663513600000000649
11,202309
12,1579821548175360000000000000769
13,(trivial factor of 59)
15,202549
16,43545601009
17,12097069
18,202729
19,43545601189
20,15920961296760632770560000000000000000000001249
22,12097369
23,12097429
24,438839318937600000000001489
25,43545601549
26,203209
27,393769398563209972074510068169201449481098556918352173620112148964244949549133907206190467334984828895355316871076009117083636780520923662813598354443998931321515584635671891365271355834108131954442039194796452662249576087338013973280335640663780129596229993141561665027264712661995223080071542562945855136153140271526716432372295748613901305709330327823699068831518910889066496000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001669
29,725761789
30,203449
31,12097909
32,203569
33,725762029
34,156764160002089
36,203809
37,203869
38,725762329
39,203989
40,7485796941752491077989753746882560000000000000000000000000000000000002449
41,43545602509
43,725762629
44,156764160002689
45,7313988648960000000002749
46,12098809
47,43545602869
48,7485796941752491077989753746882560000000000000000000000000000000000002929
50,12099049
51,725763109
52,140121763265938537447937873720739226926078690331074652274769844785983881775031005160249279556824173287142353778948596279311875900939698176000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003169
53,12099229
54,73708154151669596160000000000000000003289
55,12099349
57,205069
58,205129
59,12099589

sweety439 · 2020-11-29, 09:12

Quote:

Originally Posted by sweety439

There are still these families:

* x:{0}:(69-x):y:49 (both x and y are divisible by 7)
* x:{0}:y:(69-x):49 (both x and y are divisible by 7)
* 46:46:{42}:49
* x:46:{42}:49 (x is divisible by 7)
* 46:x:{42}:49 (x is divisible by 7)

For the families

* x:{0}:(69-x):y:49 (both x and y are divisible by 7)
* x:{0}:y:(69-x):49 (both x and y are divisible by 7)

the formula is x*60^n+(69-x)*3600+y*60+49, and the exponent n must be >=3

Code:

14,14,30474952704000000198889
14,21,3223309
14,28,3223729
14,35,39191040200149
14,42,507915878400000200569
14,49,181640989
14,56,181641409
21,14,4709689
21,21,3527193600174109
21,28,16329774529
21,35,4710949
21,42,592433080565760000000000175369
21,49,4711789
21,56,366636387458016977907728122767084862675353600000000000000000000000000000000000000000000000176209
28,14,282175488000148489
28,21,6196909
28,28,282175488000149329
28,35,21772949749
28,42,6198169
28,49,1015831756800000150589
28,56,811595095103989852199754334506901252037658952536546715570377242634958349479237785790235037396561504839643390299093296141925888112898373496415048016409202885079874806616375810473697072981470141047462017636334871127550253811801712618213586079953084484967040245525358051328000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000151009
35,14,27216123289
35,21,27216123709
35,28,5878656000124129
35,35,7684549
35,42,5878656000124969
35,49,7685389
35,56,7685809
42,14,544418089
42,21,544418509
42,28,9170929
42,35,32659299349
42,42,9171769
42,49,7054387200100189
42,56,9172609
49,14,1382343854653440000000000072889
49,21,635113309
49,28,635113729
49,35,10658149
49,42,10658569
49,49,38102474989
49,56,10659409
56,14,12143689
56,21,43545648109
56,28,5687357573431296000000000000048529
56,35,9405849600048949
56,42,121899810816000000049369
56,49,15920961296760632770560000000000000000000049789
56,56,2612736050209

sweety439 · 2020-11-29, 09:16

Quote:

Originally Posted by sweety439

For the families

* x:{0}:(69-x):y:49 (both x and y are divisible by 7)
* x:{0}:y:(69-x):49 (both x and y are divisible by 7)

the formula is x*60^n+(69-x)*3600+y*60+49, and the exponent n must be >=3

Code:

14,14,30474952704000000198889
14,21,3223309
14,28,3223729
14,35,39191040200149
14,42,507915878400000200569
14,49,181640989
14,56,181641409
21,14,4709689
21,21,3527193600174109
21,28,16329774529
21,35,4710949
21,42,592433080565760000000000175369
21,49,4711789
21,56,366636387458016977907728122767084862675353600000000000000000000000000000000000000000000000176209
28,14,282175488000148489
28,21,6196909
28,28,282175488000149329
28,35,21772949749
28,42,6198169
28,49,1015831756800000150589
28,56,811595095103989852199754334506901252037658952536546715570377242634958349479237785790235037396561504839643390299093296141925888112898373496415048016409202885079874806616375810473697072981470141047462017636334871127550253811801712618213586079953084484967040245525358051328000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000151009
35,14,27216123289
35,21,27216123709
35,28,5878656000124129
35,35,7684549
35,42,5878656000124969
35,49,7685389
35,56,7685809
42,14,544418089
42,21,544418509
42,28,9170929
42,35,32659299349
42,42,9171769
42,49,7054387200100189
42,56,9172609
49,14,1382343854653440000000000072889
49,21,635113309
49,28,635113729
49,35,10658149
49,42,10658569
49,49,38102474989
49,56,10659409
56,14,12143689
56,21,43545648109
56,28,5687357573431296000000000000048529
56,35,9405849600048949
56,42,121899810816000000049369
56,49,15920961296760632770560000000000000000000049789
56,56,2612736050209

the family x:{0}:y:(69-x):49

Code:

14,14,1828497162240000000053749
14,21,3102949
14,28,87314335528601055933672487703638179840000000000000000000000000000000000000000104149
14,35,23697323222630400000000000129349
14,42,653184154549
14,49,10886579749
14,56,1421839393357824000000000000204949
21,14,4589329
21,21,471497411854445702041831433599646171136000000000000000000000000000000000000000000078529
21,28,272263729
21,35,761873817600000128929
21,42,272314129
21,49,4715329
21,56,979776204529
28,14,47394646445260800000000000052909
28,21,21772878109
28,28,1306368103309
28,35,1015831756800000128509
28,42,6201709
28,49,363058909
28,56,6252109
35,14,7612489
35,21,453677689
35,28,453702889
35,35,453728089
35,42,1034321545091688435630547680926659383584965263068076441600000000000000000000000000000000000000000000000000000000000000000153289
35,49,453778489
35,56,7763689
42,14,9124069
42,21,1535565253221389061599916669552741110897456632189955692192083681474829512272135129453510922525361221690477166314271723033120188802017840969135872571387935377488607242892909787410267763689425664432463903752046585965934041592221392289259925461699783631470003583650680234108357136242629037178594940076711634387530300209453418542748194570067935682926374815357451554271990640558506156240804286643522510255672570190067061858896266865292979492043550504659720216667943567422442954337288192000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000077269
42,28,32659302469
42,35,544447669
42,42,117573120152869
42,49,32659378069
42,56,32659403269
49,14,137168640051649
49,21,3869678092962653798400000000000000000076849
49,28,137168640102049
49,35,10711249
49,42,237634695574640633829083042534221670252544000000000000000000000000000000000000000000000152449
49,49,10761649
49,56,1382343854653440000000000202849
56,14,566535196960657629448499885738460574873117973650423757487464494926592599020095087950406759426690829879145778405826838856593058244296318326568243605199392115332255985874049174289486092523862589770124229194573292876887438699211884282069693077913600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000051229
56,21,564350976000076429
56,28,2612736101629
56,35,(unknown)
56,42,438839318937600000000152029
56,49,12273229
56,56,43545802429

sweety439 · 2020-11-29, 09:23

Now, the unsolved families are:

{56}:5:49 (not needed, since 5 is prime)
{56}:44:49 (very low weight but eventually should yield a prime)
56:{0}:35:13:49 (not needed, since 13 is prime)

sweety439 · 2020-11-29, 11:17

Quote:

Originally Posted by sweety439

Now, the unsolved families are:

{56}:5:49 (not needed, since 5 is prime)
{56}:44:49 (very low weight but eventually should yield a prime)
56:{0}:35:13:49 (not needed, since 13 is prime)

No, 44:49 is prime (equals 2689), thus {56}:44:49 also not needed.

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2020-11-26, 04:41	#68
sweety439 Nov 2016 2²×691 Posts	There are still these families: * x:{0}:(69-x):y:49 (both x and y are divisible by 7) * x:{0}:y:(69-x):49 (both x and y are divisible by 7) * 46:46:{42}:49 * x:46:{42}:49 (x is divisible by 7) * 46:x:{42}:49 (x is divisible by 7)

2020-11-29, 09:23	#76
sweety439 Nov 2016 5314₈ Posts	Now, the unsolved families are: {56}:5:49 (not needed, since 5 is prime) {56}:44:49 (very low weight but eventually should yield a prime) 56:{0}:35:13:49 (not needed, since 13 is prime)