This version is not peer-reviewed.
Submitted:
03 February 2023
Posted:
10 February 2023
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A peer-reviewed article of this preprint also exists.
MSC: 11A41, 11A51
Algorithm 1: WFM [33] |
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Algorithm 2: FactorBasis [33] |
1 Input: A composite integer
2 if return 2
3 if return 3
4 if return 5
5 if return 7
6 Otherwise return 1
7 Output: Either a prime number or 1.
|
Algorithm 3: Forward Wheel Factoring Method (FWFM) [33] |
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Algorithm 4: TurnTest [33] |
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Algorithm 5: Backward Wheel Factoring Method (BWFM) [33] |
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Algorithm 6: NewFactorBasis |
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Algorithm 7: NewTurnTest |
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Algorithm 8: Modified Wheel Factorization Method (MWFM) |
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Turn no. | init | |||||||
---|---|---|---|---|---|---|---|---|
1 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 |
2 | 41 | 43 | 47 | 49 | 53 | 59 | 61 | 67 |
3 | 71 | 73 | 77 | 79 | 83 | 89 | 91 | 97 |
4 | 101 | 103 | 107 | 109 | 113 | 119 | 121 | 127 |
5 | 131 | 133 | 137 | 139 | 143 | 149 | 151 | 157 |
6 | 161 | 163 | 167 | 169 | 173 | 179 | 181 | 187 |
7 | 191 | 193 | 197 | 199 | 203 | 209 | 211 | 217 |
8 | 221 | 223 | 227 | 229 | 233 | 239 | 241 | 247 |
9 | 251 | 253 | 257 | 259 | 263 | 269 | 271 | 277 |
10 | 281 | 283 | 287 | 289 | 293 | 299 | 301 | 307 |
11 | 311 | 313 | 317 | 319 | 323 | 329 | 331 | 337 |
12 | 341 | 343 | 347 | 349 | 353 | 359 | 361 | 367 |
13 | 371 | 373 | 377 | 379 | 383 | 389 | 391 | 397 |
14 | 401 | 403 | 407 | 409 | 413 | 419 | 421 | 427 |
15 | 431 | 433 | 437 | 439 | 443 | 449 | 451 | 457 |
No. of digits | BWFM | MWFM |
---|---|---|
11 | 0.003 | 0.003 |
12 | 0.013 | 0.005 |
13 | 0.05 | 0.01 |
14 | 0.08 | 0.02 |
15 | 0.27 | 0.07 |
16 | 1.07 | 0.27 |
17 | 3.35 | 0.85 |
18 | 17.2 | 3.5 |
19 | 43.6 | 8.3 |
20 | 114 | 28.8 |
No. of digits | Improvement |
---|---|
11 | 0% |
12 | 62% |
13 | 80% |
14 | 75% |
15 | 74% |
16 | 75% |
17 | 75% |
18 | 80% |
19 | 81% |
20 | 75% |
Average | 75% |
No. of digits | MWFM with wheel size: | ||||
---|---|---|---|---|---|
4 | 5 | 6 | 7 | 8 | |
18 | 15.7 | 9.2 | 6.2 | 4.6 | 3.5 |
19 | 31.3 | 17.8 | 12.5 | 8.8 | 8.3 |
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