Update the newest file of [URL="https://docs.google.com/document/d/e/2PACX-1vSbzPtWAyGntyR3WQO84qPkJA6uzGsRrNjUi0BYj-iNUzGsMbeeJ9-JixXFozfODnoa8lgHhw7d3mEX/pub"]Sierpinski conjectures[/URL] to include S24 and S112

Update the newest file of [URL="https://docs.google.com/document/d/e/2PACX-1vQNX5pWcMT_ofcaNRQXpVAR8IsUI3-GmAD-Muy6rtFsym6pQN0buUOEJ3ArTaj6RKDAVNmnPhacSpVs/pub"]Riesel conjectures[/URL] to include R24 and R112

Update the newest zip file to include SR24 and SR112

[QUOTE=sweety439;546502]Update the newest file of [URL="https://docs.google.com/document/d/e/2PACX-1vQNX5pWcMT_ofcaNRQXpVAR8IsUI3-GmAD-Muy6rtFsym6pQN0buUOEJ3ArTaj6RKDAVNmnPhacSpVs/pub"]Riesel conjectures[/URL] to include R24 and R112[/QUOTE]

Corrected the file, delete "main page"

[URL="https://docs.google.com/document/d/e/2PACX-1vRhLDPjRFKjlall8eUEwdziYsZgf35Ii5Bb1Dl6erTIsUVqCQ_8_tQWuNPpQJOxyFqKxIn0CBE8wc76/pub"]https://docs.google.com/document/d/e/2PACX-1vRhLDPjRFKjlall8eUEwdziYsZgf35Ii5Bb1Dl6erTIsUVqCQ_8_tQWuNPpQJOxyFqKxIn0CBE8wc76/pub[/URL]

[QUOTE=sweety439;546507]Corrected the file, delete "main page"

[URL="https://docs.google.com/document/d/e/2PACX-1vRhLDPjRFKjlall8eUEwdziYsZgf35Ii5Bb1Dl6erTIsUVqCQ_8_tQWuNPpQJOxyFqKxIn0CBE8wc76/pub"]https://docs.google.com/document/d/e/2PACX-1vRhLDPjRFKjlall8eUEwdziYsZgf35Ii5Bb1Dl6erTIsUVqCQ_8_tQWuNPpQJOxyFqKxIn0CBE8wc76/pub[/URL][/QUOTE]

corrected the size of the exponent "n"

[URL="https://docs.google.com/document/d/e/2PACX-1vTo6WpQlMUirkqiTRqGa_XrCO1JpZHKk2gNR5cVp06vojJWzF9Z7KhF1oDb9bzK1_r_JmuSz1bAZiey/pub"]https://docs.google.com/document/d/e/2PACX-1vTo6WpQlMUirkqiTRqGa_XrCO1JpZHKk2gNR5cVp06vojJWzF9Z7KhF1oDb9bzK1_r_JmuSz1bAZiey/pub[/URL]

There are many k's that are prove composite by [B]partial algebra factors[/B] for Riesel bases:

In addition to having full algebraic factors on k's and bases that are perfect squares, there are k's that are perfect squares for many bases that are NOT perfect squares that have a numeric prime factor (p) that combines with algebraic factors to make a full covering set in the following scenarios:

[B]For any prime p and any base b, for the following set of conditions:[/B]
b==(p-1 mod p)
-and-
p==(1 mod 4)
-and-
k=m^2
-and-
m==(x or y mod p)
-and-
x+y = p

(x and y are the unique two solutions of w^2=-1 in the field Z_p)

[B]That f is a prime factor on odd-n and algebraic factors of the form [m*b^(n/2)-1]*[m*b^(n/2)+1] are present on even-n and that these combine to make a full covering set for the form k*b^n-1.[/B]

Also,

[B]For any base b, for the following set of conditions:[/B]
b==((2^r)/2+1 mod 2^r)
-and-
r>=4
-and-
k=m^2
-and-
m==((2^r)/4-1 or (2^r)/4+1 mod (2^r)/2)

[B]That 2 is a prime factor on odd-n and algebraic factors of the form [m*b^(n/2)-1]*[m*b^(n/2)+1] are present on even-n and that these combine to make a full covering set for the form (k*b^n-1)/gcd(k-1,b-1)[/B]

Listing for all factors up to 1040:

(let k=m^2 and m==(x or y mod x+y), then (k*b^n-1)/gcd(k-1,b-1) is proven composite by partial algebraic factors)

[code]
bases b== factor x & y-values
4mod5 5 2, 3
12mod13 13 5, 8
9mod16 2 3, 5
16mod17 17 4, 13
28mod29 29 12, 17
17mod32 2 7, 9
36mod37 37 6, 31
40mod41 41 9, 32
52mod53 53 23, 30
60mod61 61 11, 50
33mod64 2 15, 17
72mod73 73 27, 46
88mod89 89 34, 55
96mod97 97 22, 75
100mod101 101 10, 91
108mod109 109 33, 76
112mod113 113 15, 98
65mod128 2 31, 33
136mod137 137 37, 100
148mod149 149 44, 105
156mod157 157 28, 129
172mod173 173 80, 93
180mod181 181 19, 162
192mod193 193 81, 112
196mod197 197 14, 183
228mod229 229 107, 122
232mod233 233 89, 144
240mod241 241 64, 177
129mod256 2 63, 65
256mod257 257 16, 241
268mod269 269 82, 187
276mod277 277 60, 217
280mod281 281 53, 228
292mod293 293 138, 155
312mod313 313 25, 288
316mod317 317 114, 203
336mod337 337 148, 189
348mod349 349 136, 213
352mod353 353 42, 311
372mod373 373 104, 269
388mod389 389 115, 274
396mod397 397 63, 334
400mod401 401 20, 381
408mod409 409 143, 266
420mod421 421 29, 392
432mod433 433 179, 254
448mod449 449 67, 382
456mod457 457 109, 348
460mod461 461 48, 413
508mod509 509 208, 301
257mod512 2 127, 129
520mod521 521 235, 286
540mod541 541 52, 489
556mod557 557 118, 439
568mod569 569 86, 483
576mod577 577 24, 553
592mod593 593 77, 516
600mod601 601 125, 476
612mod613 613 35, 578
616mod617 617 194, 423
640mod641 641 154, 487
652mod653 653 149, 504
660mod661 661 106, 555
672mod673 673 58, 615
676mod677 677 26, 651
700mod701 701 135, 566
708mod709 709 96, 613
732mod733 733 353, 380
756mod757 757 87, 670
760mod761 761 39, 722
768mod769 769 62, 707
772mod773 773 317, 456
796mod797 797 215, 582
808mod809 809 318, 491
820mod821 821 295, 526
828mod829 829 246, 583
852mod853 853 333, 520
856mod857 857 207, 650
876mod877 877 151, 726
880mod881 881 387, 494
928mod929 929 324, 605
936mod937 937 196, 741
940mod941 941 97, 844
952mod953 953 442, 511
976mod977 977 252, 725
996mod997 997 161, 836
1008mod1009 1009 469, 540
1012mod1013 1013 45, 968
1020mod1021 1021 374, 647
513mod1024 2 255, 257
1032mod1033 1033 355, 678
[/code]

R96 has 176 k's remain, I forgot to remove the k's that are proven composite by partial algebraic factors, except 484

Also, (1*51^4229-1)/gcd(1-1,51-1) and (1*91^4421-1)/gcd(1-1,91-1) are now proven prime.

[URL="https://docs.google.com/document/d/e/2PACX-1vR2a7McDhmHgVS19eavqvFBORwD76nKsoUoAvsIb0NJGZ1T1vJnIGkEDkOKXetlipmFaDCO6O96a075/pub"]https://docs.google.com/document/d/e/2PACX-1vR2a7McDhmHgVS19eavqvFBORwD76nKsoUoAvsIb0NJGZ1T1vJnIGkEDkOKXetlipmFaDCO6O96a075/pub[/URL]

[QUOTE=sweety439;489690]However, k = 486, 5625, 14161, and 29584 are proven composite by partial algebraic factors.

Thus, there are 176 k's remain for k not in CRUS:

{431, 486, 591, 701, 831, 956, 1006, 1126, 1681, 2036, 2386, 3001, 3431, 3461, 3671, 3856, 3881, 3956, 3996, 4261, 4351, 4366, 4406, 4451, 4461, 5046, 5625, 5836, 6031, 6261, 6481, 6586, 6670, 6786, 7091, 7116, 7121, 7131, 7461, 7801, 8016, 8291, 8546, 8816, 9131, 9156, 9216, 9326, 9441, 9463, 9476, 9681, 9921, 10036, 10204, 10375, 10551, 10651, 10721, 11056, 11156, 11196, 11458, 11553, 11766, 11831, 12676, 12901, 13216, 13231, 13571, 14011, 14061, 14161, 14276, 14517, 14551, 14646, 15341, 15461, 15596, 16176, 16306, 16586, 16641, 16645, 17116, 17421, 17636, 18311, 19136, 19191, 19246, 19486, 19681, 20091, 20396, 20464, 20502, 20936, 21776, 22541, 22811, 22846, 22931, 23010, 23161, 23271, 23301, 23766, 24076, 24216, 24386, 24506, 24831, 24916, 24929, 25306, 25706, 25966, 26161, 26183, 26571, 26772, 26801, 26846, 27106, 27126, 27646, 27741, 28558, 28776, 28921, 29196, 29561, 29584, 29681, 30086, 30151, 30421, 30581, 31021, 31136, 31936, 32881, 33099, 33141, 33391, 33406, 33501, 33621, 33701, 33711, 33951, 33986, 34116, 34236, 34436, 34531, 34921, 35016, 35113, 35271, 35406, 35446, 35781, 35966, 36158, 36551, 36981, 37031, 37036, 37166, 37222, 37471, 37991, 38156, 38301, 38316, 38986}[/QUOTE]

R96 has 176 k's remain for k not in CRUS:

{431, 591, 701, 831, 872, 956, 1006, 1126, 1648, 1681, 1810, 2036, 2386, 2424, 2878, 3001, 3431, 3461, 3671, 3856, 3881, 3956, 3996, 4261, 4351, 4366, 4406, 4451, 4461, 5046, 5836, 5918, 6031, 6261, 6481, 6586, 6670, 6786, 7091, 7116, 7121, 7131, 7249, 7274, 7461, 7801, 8016, 8202, 8291, 8546, 8816, 9022, 9131, 9156, 9216, 9326, 9441, 9463, 9476, 9677, 9681, 9921, 10036, 10204, 10375, 10453, 10551, 10651, 10721, 11056, 11156, 11196, 11458, 11553, 11766, 11831, 12676, 12901, 13216, 13231, 13288, 13571, 14011, 14061, 14276, 14517, 14551, 14646, 15341, 15461, 15573, 15596, 16176, 16306, 16392, 16586, 16641, 16645, 17116, 17421, 17636, 17653, 17792, 18311, 19136, 19191, 19246, 19486, 19681, 20091, 20396, 20464, 20502, 20936, 21488, 21776, 22541, 22811, 22846, 22931, 23010, 23161, 23271, 23301, 23570, 23766, 24076, 24216, 24386, 24506, 24831, 24916, 24929, 25306, 25706, 25966, 26038, 26161, 26183, 26571, 26772, 26801, 26846, 27045, 27106, 27126, 27450, 27646, 27700, 27741, 28365, 28558, 28774, 28776, 28921, 29093, 29196, 29561, 29681, 30086, 30120, 30151, 30421, 30581, 30662, 31021, 31136, 31936, 32205, 32881, 33099, 33141, 33391, 33406, 33501, 33621, 33701, 33711, 33951, 33986, 34116, 34236, 34436, 34531, 34921, 35016, 35113, 35271, 35406, 35446, 35781, 35966, 36158, 36551, 36945, 36981, 37031, 37036, 37166, 37222, 37471, 37991, 38156, 38301, 38316, 38986}

[QUOTE=sweety439;546582]

Also, (1*51^4229-1)/gcd(1-1,51-1) and (1*91^4421-1)/gcd(1-1,91-1) are now proven prime.

[/QUOTE]

Primality proof certifate:

(1*51^4229-1)/gcd(1-1,51-1): [URL="http://factordb.com/cert.php?id=1100000000467236538"]http://factordb.com/cert.php?id=1100000000467236538[/URL]

(1*91^4421-1)/gcd(1-1,91-1): [URL="http://factordb.com/cert.php?id=1100000000651917018"]http://factordb.com/cert.php?id=1100000000651917018[/URL]

In Riesel conjectures, if k=m^2 or k*b=m^2 and m and b satisfy at least one of these conditions, then this k should be excluded from the Riesel base b problem, since it has algebraic factors for even n (for the k=m^2 case) or odd n (for k*b=m^2 case) and it has a single prime factor for odd n (for the k=m^2 case) or even n (for the k*b=m^2 case).

[CODE]
m b
= 2 or 3 mod 5 = 4 mod 5
= 5 or 8 mod 13 = 12 mod 13
= 3 or 5 mod 8 = 9 mod 16
= 4 or 13 mod 17 = 16 mod 17
= 12 or 17 mod 29 = 28 mod 29
= 7 or 9 mod 16 = 17 mod 32
= 6 or 31 mod 37 = 36 mod 37
= 9 or 32 mod 41 = 40 mod 41
= 23 or 30 mod 53 = 52 mod 53
= 11 or 50 mod 61 = 60 mod 61
= 15 or 17 mod 32 = 33 mod 64
= 27 or 46 mod 73 = 72 mod 73
= 34 or 55 mod 89 = 88 mod 89
= 22 or 75 mod 97 = 96 mod 97
= 10 or 91 mod 101 = 100 mod 101
= 33 or 76 mod 109 = 108 mod 109
= 15 or 98 mod 113 = 112 mod 113
= 31 or 33 mod 64 = 65 mod 128
= 37 or 100 mod 137 = 136 mod 137
= 44 or 105 mod 149 = 148 mod 149
= 28 or 129 mod 157 = 156 mod 157
= 80 or 93 mod 173 = 172 mod 173
= 19 or 162 mod 181 = 180 mod 181
= 81 or 112 mod 193 = 192 mod 193
= 14 or 183 mod 197 = 196 mod 197
= 107 or 122 mod 229 = 228 mod 229
= 89 or 144 mod 233 = 232 mod 233
= 64 or 177 mod 241 = 240 mod 241
= 63 or 65 mod 128 = 129 mod 256
= 16 or 241 mod 257 = 256 mod 257
etc.
[/CODE]

Since these k's proven composite by partial algebraic factors.

In Riesel conjectures, if k=m^2 and m and b satisfy at least one of these conditions, then this k should be excluded from the Riesel base b problem, since it has algebraic factors for even n and it has a single prime factor for odd n, thus proven composite by partial algebraic factors

list all such mod <= 2048

[CODE]
m b
= 2 or 3 mod 5 = 4 mod 5
= 3 or 5 mod 8 = 9 mod 16
= 5 or 8 mod 13 = 12 mod 13
= 7 or 9 mod 16 = 17 mod 32
= 4 or 13 mod 17 = 16 mod 17
= 12 or 17 mod 29 = 28 mod 29
= 15 or 17 mod 32 = 33 mod 64
= 6 or 31 mod 37 = 36 mod 37
= 9 or 32 mod 41 = 40 mod 41
= 23 or 30 mod 53 = 52 mod 53
= 11 or 50 mod 61 = 60 mod 61
= 31 or 33 mod 64 = 65 mod 128
= 27 or 46 mod 73 = 72 mod 73
= 34 or 55 mod 89 = 88 mod 89
= 22 or 75 mod 97 = 96 mod 97
= 10 or 91 mod 101 = 100 mod 101
= 33 or 76 mod 109 = 108 mod 109
= 15 or 98 mod 113 = 112 mod 113
= 63 or 65 mod 128 = 129 mod 256
= 37 or 100 mod 137 = 136 mod 137
= 44 or 105 mod 149 = 148 mod 149
= 28 or 129 mod 157 = 156 mod 157
= 80 or 93 mod 173 = 172 mod 173
= 19 or 162 mod 181 = 180 mod 181
= 81 or 112 mod 193 = 192 mod 193
= 14 or 183 mod 197 = 196 mod 197
= 107 or 122 mod 229 = 228 mod 229
= 89 or 144 mod 233 = 232 mod 233
= 64 or 177 mod 241 = 240 mod 241
= 127 or 129 mod 256 = 257 mod 512
= 16 or 241 mod 257 = 256 mod 257
= 82 or 187 mod 269 = 268 mod 269
= 60 or 217 mod 277 = 276 mod 277
= 53 or 228 mod 281 = 280 mod 281
= 138 or 155 mod 293 = 292 mod 293
= 25 or 288 mod 313 = 312 mod 313
= 114 or 203 mod 317 = 316 mod 317
= 148 or 189 mod 337 = 336 mod 337
= 136 or 213 mod 349 = 348 mod 349
= 42 or 311 mod 353 = 352 mod 353
= 104 or 269 mod 373 = 372 mod 373
= 115 or 274 mod 389 = 388 mod 389
= 63 or 334 mod 397 = 396 mod 397
= 20 or 381 mod 401 = 400 mod 401
= 143 or 266 mod 409 = 408 mod 409
= 29 or 392 mod 421 = 420 mod 421
= 179 or 254 mod 433 = 432 mod 433
= 67 or 382 mod 449 = 448 mod 449
= 109 or 348 mod 457 = 456 mod 457
= 48 or 413 mod 461 = 460 mod 461
= 208 or 301 mod 509 = 508 mod 509
= 255 or 257 mod 512 = 513 mod 1024
= 235 or 286 mod 521 = 520 mod 521
= 52 or 489 mod 541 = 540 mod 541
= 118 or 439 mod 557 = 556 mod 557
= 86 or 483 mod 569 = 568 mod 569
= 24 or 553 mod 577 = 576 mod 577
= 77 or 516 mod 593 = 592 mod 593
= 125 or 476 mod 601 = 600 mod 601
= 35 or 578 mod 613 = 612 mod 613
= 194 or 423 mod 617 = 616 mod 617
= 154 or 487 mod 641 = 640 mod 641
= 149 or 504 mod 653 = 652 mod 653
= 106 or 555 mod 661 = 660 mod 661
= 58 or 615 mod 673 = 672 mod 673
= 26 or 651 mod 677 = 676 mod 677
= 135 or 566 mod 701 = 700 mod 701
= 96 or 613 mod 709 = 708 mod 709
= 353 or 380 mod 733 = 732 mod 733
= 87 or 670 mod 757 = 756 mod 757
= 39 or 722 mod 761 = 760 mod 761
= 62 or 707 mod 769 = 768 mod 769
= 317 or 456 mod 773 = 772 mod 773
= 215 or 582 mod 797 = 796 mod 797
= 318 or 491 mod 809 = 808 mod 809
= 295 or 526 mod 821 = 820 mod 821
= 246 or 583 mod 829 = 828 mod 829
= 333 or 520 mod 853 = 852 mod 853
= 207 or 650 mod 857 = 856 mod 857
= 151 or 726 mod 877 = 876 mod 877
= 387 or 494 mod 881 = 880 mod 881
= 324 or 605 mod 929 = 928 mod 929
= 196 or 741 mod 937 = 936 mod 937
= 97 or 844 mod 941 = 940 mod 941
= 442 or 511 mod 953 = 952 mod 953
= 252 or 725 mod 977 = 976 mod 977
= 161 or 836 mod 997 = 996 mod 997
= 469 or 540 mod 1009 = 1008 mod 1009
= 45 or 968 mod 1013 = 1012 mod 1013
= 374 or 647 mod 1021 = 1020 mod 1021
= 511 or 513 mod 1024 = 1025 mod 2048
= 355 or 678 mod 1033 = 1032 mod 1033
= 426 or 623 mod 1049 = 1048 mod 1049
= 103 or 958 mod 1061 = 1060 mod 1061
= 249 or 820 mod 1069 = 1068 mod 1069
= 530 or 563 mod 1093 = 1092 mod 1093
= 341 or 756 mod 1097 = 1096 mod 1097
= 354 or 755 mod 1109 = 1108 mod 1109
= 214 or 903 mod 1117 = 1116 mod 1117
= 168 or 961 mod 1129 = 1128 mod 1129
= 140 or 1013 mod 1153 = 1152 mod 1153
= 243 or 938 mod 1181 = 1180 mod 1181
= 186 or 1007 mod 1193 = 1192 mod 1193
= 49 or 1152 mod 1201 = 1200 mod 1201
= 495 or 718 mod 1213 = 1212 mod 1213
= 78 or 1139 mod 1217 = 1216 mod 1217
= 597 or 632 mod 1229 = 1228 mod 1229
= 546 or 691 mod 1237 = 1236 mod 1237
= 585 or 664 mod 1249 = 1248 mod 1249
= 113 or 1164 mod 1277 = 1276 mod 1277
= 479 or 810 mod 1289 = 1288 mod 1289
= 36 or 1261 mod 1297 = 1296 mod 1297
= 51 or 1250 mod 1301 = 1300 mod 1301
= 257 or 1064 mod 1321 = 1320 mod 1321
= 614 or 747 mod 1361 = 1360 mod 1361
= 668 or 705 mod 1373 = 1372 mod 1373
= 366 or 1015 mod 1381 = 1380 mod 1381
= 452 or 957 mod 1409 = 1408 mod 1409
= 620 or 809 mod 1429 = 1428 mod 1429
= 542 or 891 mod 1433 = 1432 mod 1433
= 497 or 956 mod 1453 = 1452 mod 1453
= 465 or 1016 mod 1481 = 1480 mod 1481
= 225 or 1264 mod 1489 = 1488 mod 1489
= 432 or 1061 mod 1493 = 1492 mod 1493
= 88 or 1461 mod 1549 = 1548 mod 1549
= 339 or 1214 mod 1553 = 1552 mod 1553
= 610 or 987 mod 1597 = 1596 mod 1597
= 40 or 1561 mod 1601 = 1600 mod 1601
= 523 or 1086 mod 1609 = 1608 mod 1609
= 127 or 1486 mod 1613 = 1612 mod 1613
= 166 or 1455 mod 1621 = 1620 mod 1621
= 316 or 1321 mod 1637 = 1636 mod 1637
= 783 or 874 mod 1657 = 1656 mod 1657
= 220 or 1449 mod 1669 = 1668 mod 1669
= 92 or 1601 mod 1693 = 1692 mod 1693
= 414 or 1283 mod 1697 = 1696 mod 1697
= 390 or 1319 mod 1709 = 1708 mod 1709
= 473 or 1248 mod 1721 = 1720 mod 1721
= 410 or 1323 mod 1733 = 1732 mod 1733
= 59 or 1682 mod 1741 = 1740 mod 1741
= 713 or 1040 mod 1753 = 1752 mod 1753
= 775 or 1002 mod 1777 = 1776 mod 1777
= 724 or 1065 mod 1789 = 1788 mod 1789
= 824 or 977 mod 1801 = 1800 mod 1801
= 61 or 1800 mod 1861 = 1860 mod 1861
= 737 or 1136 mod 1873 = 1872 mod 1873
= 137 or 1740 mod 1877 = 1876 mod 1877
= 331 or 1558 mod 1889 = 1888 mod 1889
= 218 or 1683 mod 1901 = 1900 mod 1901
= 712 or 1201 mod 1913 = 1912 mod 1913
= 598 or 1335 mod 1933 = 1932 mod 1933
= 589 or 1360 mod 1949 = 1948 mod 1949
= 259 or 1714 mod 1973 = 1972 mod 1973
= 834 or 1159 mod 1993 = 1992 mod 1993
= 412 or 1585 mod 1997 = 1996 mod 1997
= 229 or 1788 mod 2017 = 2016 mod 2017
= 992 or 1037 mod 2029 = 2028 mod 2029
= 1023 or 1025 mod 2048 = 2049 mod 4096
[/CODE]