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2020-07-14, 11:57   #903
sweety439

Nov 2016

34·31 Posts

Quote:
 Originally Posted by sweety439 Found an error of S81: (34*81^734+1)/gcd(34+1,81-1) is prime Double checking S81....
There are two other errors (for k=317 and 389): (317*81^518+1)/gcd(317+1,81-1) and (389*81^871+1)/gcd(389+1,81-1) are primes

Re-update the zip file
Attached Files
 extend SR conjectures.zip (1.47 MB, 20 views)

Last fiddled with by sweety439 on 2020-07-14 at 12:24

 2020-07-14, 12:14 #904 sweety439     Nov 2016 47178 Posts Update newest status of Sierpinski problems S81 has only 7 k remain Last fiddled with by sweety439 on 2020-07-14 at 12:14
 2020-07-15, 00:25 #905 sweety439     Nov 2016 34×31 Posts These ranges are completed: "[]" for the remaining (b,k) pair such that no smaller k for this b, no smaller b for this k, no smaller b and smaller k, are remaining. (b>=2, k>=1) Sierpinski: [2,21181] b=2, k<=21180 [3,1187] b<=4, k<=1186 [5,181] b<=9, k<=180 [10,100] b<=11, k<=99 [12,12] b<=30, k<=11 [31,1] Riesel: [2,2293] b=2, k<=2292 [3,1613] b<=4, k<=1612 [5,1279] b<=6, k<=1278 [7,679] b<=7, k<=678 [8,239] b<=10, k<=238 [11,201] b<=14, k<=200 [15,47] b<=30, k<=46 [31,5] b<=158, k<=4 [159,3] b<=184, k<=2 [185,1]
2020-07-15, 21:15   #906
sweety439

Nov 2016

34·31 Posts

Quote:
 Originally Posted by sweety439 These ranges are completed: "[]" for the remaining (b,k) pair such that no smaller k for this b, no smaller b for this k, no smaller b and smaller k, are remaining.
(Probable) primes with n>=1000 and smaller (b,k):

Sierpinski:

b=2: (see http://www.prothsearch.com/sierp.html)

b=3:

k=41, n=4892 (k=123, n=4891, k=369, n=4890, k=1107, n=4889)
k=523, n=1775
k=621, n=20820
k=821, n=5512
k=823, n=6087
k=935, n=3967

b=4:

k=186, n=10458 (k=744, n=10457)
k=766, n=3196
k=839, n=1217

b=5:

k=40, n=1036
k=61, n=6208

b=6:

k=160, n=3143

b=7:

k=141, n=1044

b=8:

k=173, n=7771

b=9:

k=41, n=2446

b=17:

k=10, n=1356

b=23:

k=8, n=119215
k=10, n=3762

Riesel:

b=2: (see http://www.prothsearch.com/rieselprob.html)

b=3:

k=97, n=3131 (k=291, n=3130, k=873, n=3129)
k=119, n=8972 (k=357, n=8971, k=1071, n=8970)
k=302, n=2091 (k=906, n=2090)
k=313, n=24761 (k=939, n=24760)
k=599, n=1240
k=811, n=1126
k=997, n=20847
k=1013, n=1233
k=1093, n=1297
k=1199, n=3876
k=1303, n=1384

b=4:

k=74, n=1276 (k=296, n=1275, k=1184, n=1274)
k=106, n=4553 (k=424, n=4552)
k=373, n=2508 (k=1492, n=2507)
k=659, n=400258
k=674, n=5838
k=751, n=6615
k=1103, n=2203
k=1159, n=5628
k=1171, n=2855
k=1189, n=3404
k=1211, n=12621
k=1524, n=1994

b=5:

k=86, n=2058 (k=430, n=2057)
k=428, n=9704
k=638, n=6974
k=662, n=14628
k=935, n=1560
k=1006, n=4197

b=6:

k=251, n=3008
k=1030, n=1199

b=7:

k=159, n=4896 (k=1113, n=4895)
k=197, n=181761
k=313, n=5907
k=367, n=15118
k=419, n=1052
k=429, n=3815
k=653, n=1051

b=8:

k=74, n=2632
k=151, n=2141
k=191, n=1198
k=203, n=1866
k=236, n=5258

b=9:

k=119, n=4486

b=11:

k=62, n=26202

b=14:

k=5, n=19698 (k=70, n=19697)

b=17:

k=13, n=1123
k=29, n=4904
k=44, n=6488

b=23:

k=30, n=1000

b=26:

k=32, n=9812

b=27:

k=23, n=3742

b=30:

k=25, n=34205

b=42:

k=3, n=2523

b=47:

k=4, n=1555

b=51:

k=1, n=4229

b=72:

k=4, n=1119849

b=91:

k=1, n=4421

b=107:

k=2, n=21910
k=3, n=4900

b=115:

k=4, n=4223

b=135:

k=1, n=1171

b=142:

k=1, n=1231

b=152:

k=1, n=270217

b=170:

k=2, n=166428

b=174:

k=1, n=3251

b=184:

k=1, n=16703

Last fiddled with by sweety439 on 2020-08-08 at 16:23

2020-07-15, 23:27   #907
sweety439

Nov 2016

47178 Posts

Store the files for R42 k=3 and k=14 (3*14=42, thus they are duals)

these solved R1764 k=14, k=126=3*42, k=588=14*42, but k=3 is still unsloved
Attached Files
 pfgw.log (65 Bytes, 19 views) pfgw-prime.log (11 Bytes, 23 views)

Last fiddled with by sweety439 on 2020-07-15 at 23:28

2020-07-16, 18:06   #908
sweety439

Nov 2016

34×31 Posts

Quote:
 Originally Posted by sweety439 Sierpinski: [2,21181] b=2, k<=21180 [3,1187] b<=4, k<=1186 [5,181] b<=9, k<=180 [10,100] b<=11, k<=99 [12,12] b<=30, k<=11 [31,1]
If GFN's and half GFN's are not counted, then this list become:

[2,21181]

b=2, k<=21180

[3,1187]

b<=4, k<=1186

[5,181]

b<=15, k<=180

[16,89]

b<=16, k<=88

[17,53]

b<=26, k<=52

[27,49]

b<=30, k<=48

[31,43]

b<=40, k<=42

[41,28]

b<=46, k<=27

[47,27]

b<=52, k<=26

[53,4]

b<=82, k<=3

[83,3]

b<=364, k=2

[365,2]

(k=1 is no longer available, since k=1 for all even b are GFN's and for all odd b are half GFN's)

 2020-07-19, 11:22 #909 sweety439     Nov 2016 34·31 Posts Fixed the files - remove "color used" section - change the better name of "the top 10 k's" column: "only sorted by n" --> "sorted by n only" Sierpinski problems Riesel problems
2020-07-19, 12:06   #910
sweety439

Nov 2016

34·31 Posts

Quote:
 Originally Posted by sweety439 There are many Riesel case for k=64 (since 64 = 4^3 = 8^2, thus n == 0 mod 2 or n == 0 mod 3 have algebra factors: Bases 619, 1322, 2025, 2728, 3431, 4134, 4837, 5540, 6243, 6946, 7649, 8352, 9055, 9758, ...: n == 1 mod 3: factor of 19, n == 5 mod 6: factor of 37 Bases 429, 1816, 3203, 4590, 5977, 7364, 8751, ...: n == 1 mod 3: factor of 19, n == 2 mod 3: factor of 73 Bases 391, 2462, 4533, 6604, 8675, ...: n == 1 mod 3: factor of 19, n == 5 mod 6: factor of 109 Bases 159, 862, 1565, 2268, 2971, 3674, 4377, 5080, 5783, 6486, 7189, 7892, 8595, 9298, ...: n == 1 mod 6: factor of 37, n == 2 mod 3: factor of 19 Bases 1232, 3933, 6634, 9335, ...: n == 1 mod 6: factor of 37, n == 2 mod 3: factor of 73 Bases 936, 4969, 9002, ...: n == 1 mod 6: factor of 37, n == 5 mod 6: factor of 109 Bases 957, 2344, 3731, 5118, 6505, 7892, 9279, ...: n == 1 mod 3: factor of 73, n == 2 mod 3: factor of 19 Bases 1322, 4023, 6724, 9425, ...: n == 1 mod 3: factor of 73, n == 5 mod 6: factor of 37 Bases 4315, ...: n == 1 mod 3: factor of 73, n == 5 mod 6: factor of 109 Bases 482, 2553, 4624, 6695, 8766, ...: n == 1 mod 6: factor of 109, n == 2 mod 3: factor of 19 Bases 3098, 7131, ...: n == 1 mod 6: factor of 109, n == 5 mod 6: factor of 37 Bases 4079, ...: n == 1 mod 6: factor of 109, n == 2 mod 3: factor of 73
In fact, base 391 has covering set {3, 7, 19, 109}, and base 429 has covering set {5, 7, 19, 73}

(bases 159, 482, 619, 862, 936, 957 are unlikely to have covering set)

Last fiddled with by sweety439 on 2020-07-19 at 12:15

2020-07-22, 15:14   #911
sweety439

Nov 2016

34·31 Posts

Quote:
 Originally Posted by sweety439 If GFN's and half GFN's are not counted, then this list become: [2,21181] b=2, k<=21180 [3,1187] b<=4, k<=1186 [5,181] b<=15, k<=180 [16,89] b<=16, k<=88 [17,53] b<=26, k<=52 [27,49] b<=30, k<=48 [31,43] b<=40, k<=42 [41,28] b<=46, k<=27 [47,27] b<=52, k<=26 [53,4] b<=82, k<=3 [83,3] b<=364, k=2 [365,2] (k=1 is no longer available, since k=1 for all even b are GFN's and for all odd b are half GFN's)
and the (probable) primes with n>=1000 and smaller (b,k) are:

b=2: (see http://www.prothsearch.com/sierp.html)

b=3:

k=41, n=4892 (k=123, n=4891, k=369, n=4890, k=1107, n=4889)
k=523, n=1775
k=621, n=20820
k=821, n=5512
k=823, n=6087
k=935, n=3967

b=4:

k=186, n=10458 (k=744, n=10457)
k=766, n=3196
k=839, n=1217

b=5:

k=40, n=1036
k=61, n=6208

b=6:

k=160, n=3143

b=7:

k=141, n=1044

b=8:

k=173, n=7771

b=9:

k=41, n=2446

b=13:

k=29, n=10574
k=48, n=6267
k=120, n=1552

b=14:

k=73, n=1182
k=145, n=1176

b=16:

k=23, n=1074

b=17:

k=10, n=1356

b=20:

k=43, n=2956

b=23:

k=8, n=119215
k=10, n=3762

b=26:

k=32, n=318071

b=27:

k=33, n=7876

b=30:

k=12, n=1023

b=31:

k=5, n=1026

b=33:

k=36, n=23615

b=37:

k=19, n=5310

b=38:

k=2, n=2729
k=31, n=1528

b=45:

k=24, n=18522

b=46:

k=17, n=4920

b=101:

k=2, n=192275

b=104:

k=2, n=1233

b=167:

k=2, n=6547

b=206:

k=2, n=46205

b=218:

k=2, n=333925

b=236:

k=2, n=161229

b=257:

k=2, n=12183

b=287:

k=2, n=5467

b=305:

k=2, n=16807

b=353:

k=2, n=2313

Last fiddled with by sweety439 on 2020-07-22 at 16:25

2020-07-24, 14:39   #912
sweety439

Nov 2016

9CF16 Posts

Searched to 5M, "NA" if > 5M, almost done to base 2500 ....
Attached Files
 Conjectured smallest Sierpinski.txt (20.8 KB, 21 views) Conjectured smallest Riesel.txt (20.0 KB, 18 views)

2020-07-24, 15:41   #913
sweety439

Nov 2016

251110 Posts

Quote:
 Originally Posted by sweety439 Searched to 5M, "NA" if > 5M, almost done to base 2500 ....
Test limit:

primes in the covering set <= 100K
exponents <= 2100 (not 2000, to include 2048 = 2^11 to return the true CK for S125, otherwise it will return CK=1 for S125)

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