|
Except by k or by p, I ' d like to share another
algorithm that sort by the number p, but not by the exponent p. Suppose we want to find all the factors of number 2^n - 1. where n could be a composite. There is a simple algorithm something like this. given a prime number p [CODE]long long llMult = 1; for (i = 0; i < 10^9; i++) { llMult = (llMult * 2) mod p; if (llMult == 1) { return i; } } return (10^9 + 1);[/CODE] If the return value n is less than 10^9, then p is a factor of 2^n - 1. If the return value is larger than 10^9, then p is not the factor for all of number 2^n - 1, where n less than 10^9. It is possible that this algorithm will faster than search by k. |
This is just the exponentiation part of both "by k" or "by p", except here it is done very lousy, about 530 million times slower, in average, than the classical modular exponentiation by squaring.
Grrr... Repeat after me: I will read the [URL="https://www.mersenne.org/various/math.php"]math page[/URL] before posting stupidities on the forum... The example there (at the "Trial Factoring" section) shows you how to do 4 modular squares instead of 23 modular shifts. If your exponent is in hundreds of millions (<30 bits) you will have to do 30 modular squarings instead of hundreds of millions of modular shifts. Wake up! You do not need to do 300 millions multiplications by two (shifts, but still need the modular calculus to p), you can solve this with a couple of squarings. And you need to do this anyhow, no matter if you search "by p" or "by k". Both the methods are doing your "algorithm" already, for each k, or respective p, candidate, except that every time they do the "algorithm" few millions time faster than in your post. |
I downloaded all the factors in the database instead of relying on the xml files to compare all factors (including TJAOI) to his factors.
Here is the file if anyone else is interested: gimpsfactors20170923.7z (339 MB) (1050 MB unpacked) [url]https://mega.nz/#!0Jon1ZzI!5Np_8aFTiNnvNBBPzrXqCbHHyBzStx5UT209SscW17w[/url] Factors of the database as of 2017-09-23 at about 5am UTC. 41,154,580 factors of 29,239,422 different exponents (21,608,172 exponents < 10[sup]9[/sup] without any known factor) [CODE] ALL TJAOI Total 41154580 5736797 Bits 5 1 6 1 8 3 9 7 10 5 11 10 12 22 13 38 14 58 15 91 16 169 17 313 18 569 19 965 20 1723 21 3087 22 5569 23 10245 24 18594 25 34430 26 62674 27 116162 28 214794 29 398847 30 742758 31 1276984 32 1059682 33 1532803 34 1403266 35 1450038 36 1415679 37 1387566 38 1352136 39 1318424 40 1285766 38 41 1255615 453 42 1226519 6565 43 1195924 18833 44 1168667 38012 45 1143068 71809 46 1119457 74795 47 1093264 77168 48 1069382 82727 49 1048083 92413 50 1027616 97976 51 1008664 120260 11.9% 52 987453 149602 15.2% 53 966265 222679 23.0% 54 951288 364134 38.3% 55 932325 412526 44.2% 56 915449 412589 45.1% 57 900026 414657 46.1% 58 884371 416043 47.0% 59 869543 416701 47.9% 60 853996 417979 48.9% 61 840435 415855 49.5% 62 828086 414941 50.1% 63 813353 413842 50.9% 64 798515 420583 52.7% 65 524408 150609 28.7% 66 353283 578 67 342956 622 68 330941 587 69 215809 615 70 162764 621 71 64444 663 72 48354 645 73 22502 633 74 16185 608 75 11765 636 76 7697 633 77 6241 621 78 5727 557 79 5113 548 80 4544 475 81 4019 449 82 3794 409 83 3337 417 84 2940 341 85 2743 315 86 2426 254 87 2252 260 88 1950 223 89 1788 235 90 1549 162 91 1504 133 92 1337 123 93 1145 99 94 1054 100 95 986 69 96 836 63 97 726 48 98 709 43 99 613 43 100 509 27 101 466 26 102 447 23 103 383 16 104 361 17 105 293 13 106 279 13 107 259 8 108 192 4 109 208 8 110 185 5 111 148 4 112 144 1 113 130 3 114 116 1 115 92 3 116 88 3 117 73 118 69 119 70 1 120 53 121 62 122 48 3 123 43 124 43 125 41 126 30 127 26 128 24 129 27 130 23 131 16 132 22 1 133 17 134 13 135 16 136 4 137 19 138 8 139 13 140 8 141 8 142 9 143 9 144 8 145 7 146 8 147 10 148 7 149 8 150 3 151 1 152 12 153 4 154 4 155 4 157 3 158 3 159 3 160 3 161 2 162 4 163 2 164 5 165 2 167 4 168 1 169 1 170 3 172 3 174 3 175 1 176 3 177 1 180 1 181 1 182 2 183 2 184 2 187 2 188 1 189 1 190 1 192 1 195 2 196 2 198 2 199 1 200 1 201 1 202 1 203 1 204 2 206 2 207 2 208 1 209 1 210 1 217 2 218 1 222 1 226 1 227 1 228 3 229 1 231 1 232 1 234 1 236 1 240 1 241 2 242 1 246 1 249 1 250 1 258 1 259 1 262 1 263 1 264 1 265 1 271 1 274 1 285 1 293 1 295 1 313 1 321 1 324 1 342 1 345 1 346 1 405 1 416 1 422 1 423 1 460 1 474 1 483 1 [/CODE] |
[QUOTE=ATH;468436]I downloaded all the factors in the database instead of relying on the xml files to compare all factors (including TJAOI) to his factors.
Here is the file if anyone else is interested: gimpsfactors20170923.7z (339 MB) (1050 MB unpacked) [url]https://mega.nz/#!0Jon1ZzI!5Np_8aFTiNnvNBBPzrXqCbHHyBzStx5UT209SscW17w[/url] Factors of the database as of 2017-09-23 at about 5am UTC. 41,154,580 factors of 29,239,422 different exponents (21,608,172 exponents < 10[sup]9[/sup] without any known factor) [CODE] ALL TJAOI Total 41154580 5736797 Bits 5 1 6 1 8 3 9 7 10 5 11 10 12 22 13 38 14 58 15 91 16 169 17 313 18 569 19 965 20 1723 21 3087 22 5569 23 10245 24 18594 25 34430 26 62674 27 116162 28 214794 29 398847 30 742758 31 1276984 32 1059682 33 1532803 34 1403266 35 1450038 36 1415679 37 1387566 38 1352136 39 1318424 40 1285766 38 41 1255615 453 42 1226519 6565 43 1195924 18833 44 1168667 38012 45 1143068 71809 46 1119457 74795 47 1093264 77168 48 1069382 82727 49 1048083 92413 50 1027616 97976 51 1008664 120260 11.9% 52 987453 149602 15.2% 53 966265 222679 23.0% 54 951288 364134 38.3% 55 932325 412526 44.2% 56 915449 412589 45.1% 57 900026 414657 46.1% 58 884371 416043 47.0% 59 869543 416701 47.9% 60 853996 417979 48.9% 61 840435 415855 49.5% 62 828086 414941 50.1% 63 813353 413842 50.9% 64 798515 420583 52.7% 65 524408 150609 28.7% 66 353283 578 67 342956 622 68 330941 587 69 215809 615 70 162764 621 71 64444 663 72 48354 645 73 22502 633 74 16185 608 75 11765 636 76 7697 633 77 6241 621 78 5727 557 79 5113 548 80 4544 475 81 4019 449 82 3794 409 83 3337 417 84 2940 341 85 2743 315 86 2426 254 87 2252 260 88 1950 223 89 1788 235 90 1549 162 91 1504 133 92 1337 123 93 1145 99 94 1054 100 95 986 69 96 836 63 97 726 48 98 709 43 99 613 43 100 509 27 101 466 26 102 447 23 103 383 16 104 361 17 105 293 13 106 279 13 107 259 8 108 192 4 109 208 8 110 185 5 111 148 4 112 144 1 113 130 3 114 116 1 115 92 3 116 88 3 117 73 118 69 119 70 1 120 53 121 62 122 48 3 123 43 124 43 125 41 126 30 127 26 128 24 129 27 130 23 131 16 132 22 1 133 17 134 13 135 16 136 4 137 19 138 8 139 13 140 8 141 8 142 9 143 9 144 8 145 7 146 8 147 10 148 7 149 8 150 3 151 1 152 12 153 4 154 4 155 4 157 3 158 3 159 3 160 3 161 2 162 4 163 2 164 5 165 2 167 4 168 1 169 1 170 3 172 3 174 3 175 1 176 3 177 1 180 1 181 1 182 2 183 2 184 2 187 2 188 1 189 1 190 1 192 1 195 2 196 2 198 2 199 1 200 1 201 1 202 1 203 1 204 2 206 2 207 2 208 1 209 1 210 1 217 2 218 1 222 1 226 1 227 1 228 3 229 1 231 1 232 1 234 1 236 1 240 1 241 2 242 1 246 1 249 1 250 1 258 1 259 1 262 1 263 1 264 1 265 1 271 1 274 1 285 1 293 1 295 1 313 1 321 1 324 1 342 1 345 1 346 1 405 1 416 1 422 1 423 1 460 1 474 1 483 1 [/CODE][/QUOTE] so basically 1 in every 7 factors known. |
[QUOTE=LaurV;468434]This is just the exponentiation part of both "by k" or "by p", except here it is done very lousy, about 530 million times slower, in average, than the classical modular exponentiation by squaring.
[/QUOTE] Thanks for your respones. Your reply promote me to analyze these 3 methods more carefully. And the result surprised me a little, I admit I am wrong. The two key points I miss is that 1. (2^n-1) mod m is only need ln(n) / ln(2) times mod operation, but not n which I thought. 2. search by "number p" need 10^9 times mod operation, but not 1 which I thought. Why I thought searching by "number p" but not by "exponent n" is that, for a prime number q = 2 * k * p + 1, if q = 2 * k1 * p1 * p2 + 1, where p1 and p2 are prime, we have to calculate (2^p1 - 1) mod q and (2^p2 - 1) mod q both. [CODE]Analyse method "exponent n", "k" and "p" ' s complexity. 1. exponent n Suppose n is larger than 1000. For a single exponent n. 2^64 / ln(2^64) / n prime numbers need to calculate, each number need calculate ln(n) / ln(2) times mod. Total mod times is: (2^64 / ln(2^64) / n) * ln(n) / ln(2) = 2^64 / 64 * ln(n) / n For all the exponent n less than 10^9, total mod times is: 2^64 / 64 * ln(1000) / 1000 + 2^64 / 64 * ln(1001) / 1001 + ... + 2^64 / 64 * ln(10^9) / 10^9 = 2^64 / 64 * 191 ln(1000) / 1000 + ... + ln(10^9) / 10^9 = S ln(x) / x dx, x from 1000 to 10^9 = S ln(x) d ln(x), x from 1000 to 10^9 = 1 / 2 * [ln(x)]^2|x from 1000 to 10^9 = 1 / 2 * {[ln(10^9)]^2 - [ln(1000)]^2} = 1 / 2 * {429.5 - 47.7} = 190.9 If only consider n larger than 10^8, then total mod times is: = 2^64 / 64 * 46 Here suppose "(2^n - 1) mod m" need ln(n) / ln(2) times mod calculation. 2. k need totally mod times is also: 2^64 / 64 * 191 3. p single number's mod times is 10^9. Total mod times is: 2^64 / ln(2^64) * 10^9 = 2^64 / 64 * 1442695041 is 7553378 times slower than method search by "exponent n". [/CODE] |
[QUOTE=wreck;468465]
2. search by "number p" need 10^9 times mod operation, but not 1 which I thought. Why I thought searching by "number p" but not by "exponent n" is that, for a prime number q = 2 * k * p + 1, if q = 2 * k1 * p1 * p2 + 1, where p1 and p2 are prime, we have to calculate (2^p1 - 1) mod q and (2^p2 - 1) mod q both. [/QUOTE] Yes, somehow like that, with the difference that when you search "by p" (like GIMPS does) you only have the prime p, and once you get a factor, you eliminate that p. Therefore, you start with about 50 million (5*10^7) and not 10^9. From which GIMPS already eliminated more than half ([URL="http://www.mersenne.ca/status/tf/0/0/1/0"]only about 21.6 millions left[/URL]). Disadvantage is that you only find first (or first few) factors for a given p. Of course, you can continue higher than that, if you want, but yet, only candidates of the form 2kp+1 will be tested (we do not talk here about putting them in classes and sieving, which also eliminates a lot of them). When you search "by k", you still have to examine all candidates, because you do not know in advance whose exponent p mersenne, some candidate q turns out to factor, unless you factor q-1, or so. Some candidates q=2x+1, after factoring x, and/or make the list of its divisors, it will turn out that they divide a 2^n+1 for a non-prime n, or for n>10^9. In fact, most of them turn out that way, dividing exactly 2^x+1, and therefore x>10^9 for factors over 2^32). You have to do a lot of additional work. Advantage is that you find all the factors for a bitlevel, for all possible k AND p, but you have to do much MUCH more work. |
For each fixed k you can create an array of all the primes p<10^9 and then sieve that array. For each sieve prime q, you find the smallest p for which 2kp+1=0 (mod q) by the extended Euclidean algorithm, lets call it p1, and then you remove all the p1, p1+q, p1+2q... up to 10^9 from the array.
Once you reach a suitable high q where further trial factoring is slower than testing candidates, you test if the remaining 2kp+1 are factors of 2^p-1. Edit: Before (or after) you sieve the array you remove all the p for which 2kp+1 is not equal to 1,7,17,23,31,41,47,49,71,73,79,89,97,103,113,119 (mod 120). |
[QUOTE=LaurV;468434]This is just the exponentiation part of both "by k" or "by p", except here it is done very lousy, about 530 million times slower, in average, than the classical modular exponentiation by squaring.
Grrr... Repeat after me: I will read the [URL="https://www.mersenne.org/various/math.php"]math page[/URL] before posting stupidities on the forum... The example there (at the "Trial Factoring" section) shows you how to do 4 modular squares instead of 23 modular shifts. If your exponent is in hundreds of millions (<30 bits) you will have to do 30 modular squarings instead of hundreds of millions of modular shifts. Wake up! You do not need to do 300 millions multiplications by two (shifts, but still need the modular calculus to p), you can solve this with a couple of squarings. And you need to do this anyhow, no matter if you search "by p" or "by k". Both the methods are doing your "algorithm" already, for each k, or respective p, candidate, except that every time they do the "algorithm" few millions time faster than in your post.[/QUOTE] You sound like RDS |
[QUOTE=petrw1;468271]How hard would it be to note how many "FIRST" factors he found?[/QUOTE]
TJAOI actually found 827 first factors that I can find (see full lists below). 612 of those from his normal factoring project, and on exponents where previous factoring had occured, but which failed to find them, which seems strange. Either the low bit level he found them on are NOT listed as having been done before even though higher levels has, examples: [url]https://mersenne.org/M33088541[/url] [url]https://mersenne.org/M371038891[/url] or the same bit level had been factored before but apparantly missed the factor? Examples: [url]https://mersenne.org/M270084769[/url] [url]https://mersenne.org/M370825747[/url] or exponents where no factoring had ever been done, even though the range 100M-1000M should have been done to low level at least back in 2008-2010 when the v5 server was new, examples: [url]https://mersenne.org/M415560947[/url] [url]https://mersenne.org/M428160451[/url] He also found 8 first factors by trial factoring at higher bit levels outside his normal project, where he was actually the first to trial factor that range, maybe on a GPU? and he has found 207 first factors by ECM. Trial factoring (612 exponents): [CODE] [URL]https://mersenne.org/M6811111[/URL] [url]https://mersenne.org/M7024807[/url] [url]https://mersenne.org/M7028183[/url] [url]https://mersenne.org/M7043441[/url] [url]https://mersenne.org/M7047839[/url] [url]https://mersenne.org/M7763923[/url] [url]https://mersenne.org/M8154967[/url] [url]https://mersenne.org/M8613757[/url] [url]https://mersenne.org/M9371851[/url] [url]https://mersenne.org/M10465573[/url] [url]https://mersenne.org/M10635311[/url] [url]https://mersenne.org/M13128419[/url] [url]https://mersenne.org/M15470531[/url] [url]https://mersenne.org/M16361909[/url] [url]https://mersenne.org/M16556363[/url] [url]https://mersenne.org/M16684181[/url] [url]https://mersenne.org/M16686841[/url] [url]https://mersenne.org/M17458547[/url] [url]https://mersenne.org/M17458939[/url] [url]https://mersenne.org/M17459069[/url] [url]https://mersenne.org/M17752381[/url] [url]https://mersenne.org/M17841221[/url] [url]https://mersenne.org/M17959243[/url] [url]https://mersenne.org/M17977189[/url] [url]https://mersenne.org/M18954283[/url] [url]https://mersenne.org/M25257509[/url] [url]https://mersenne.org/M28000339[/url] [url]https://mersenne.org/M32712703[/url] [url]https://mersenne.org/M33088541[/url] [url]https://mersenne.org/M33122153[/url] [url]https://mersenne.org/M33142423[/url] [url]https://mersenne.org/M33708737[/url] [url]https://mersenne.org/M47630519[/url] [url]https://mersenne.org/M66104189[/url] [url]https://mersenne.org/M66195611[/url] [url]https://mersenne.org/M66219407[/url] [url]https://mersenne.org/M88611311[/url] [url]https://mersenne.org/M90751757[/url] [url]https://mersenne.org/M95687831[/url] [url]https://mersenne.org/M98357197[/url] [url]https://mersenne.org/M98509891[/url] [url]https://mersenne.org/M99492737[/url] [url]https://mersenne.org/M102000401[/url] [url]https://mersenne.org/M107179573[/url] [url]https://mersenne.org/M109086547[/url] [url]https://mersenne.org/M109252799[/url] [url]https://mersenne.org/M113001529[/url] [url]https://mersenne.org/M113264699[/url] [url]https://mersenne.org/M115488017[/url] [url]https://mersenne.org/M115647463[/url] [url]https://mersenne.org/M118267993[/url] [url]https://mersenne.org/M124662107[/url] [url]https://mersenne.org/M129637633[/url] [url]https://mersenne.org/M131028587[/url] [url]https://mersenne.org/M132131101[/url] [url]https://mersenne.org/M132150919[/url] [url]https://mersenne.org/M132308147[/url] [url]https://mersenne.org/M132343297[/url] [url]https://mersenne.org/M132377899[/url] [url]https://mersenne.org/M132385271[/url] [url]https://mersenne.org/M132395539[/url] [url]https://mersenne.org/M132545783[/url] [url]https://mersenne.org/M132833819[/url] [url]https://mersenne.org/M138733691[/url] [url]https://mersenne.org/M139651271[/url] [url]https://mersenne.org/M147603019[/url] [url]https://mersenne.org/M153177001[/url] [url]https://mersenne.org/M156526709[/url] [url]https://mersenne.org/M165789791[/url] [url]https://mersenne.org/M171084343[/url] [url]https://mersenne.org/M181038499[/url] [url]https://mersenne.org/M184668401[/url] [url]https://mersenne.org/M184811321[/url] [url]https://mersenne.org/M188141959[/url] [url]https://mersenne.org/M188376091[/url] [url]https://mersenne.org/M188376691[/url] [url]https://mersenne.org/M188377817[/url] [url]https://mersenne.org/M188385983[/url] [url]https://mersenne.org/M188398271[/url] [url]https://mersenne.org/M188403289[/url] [url]https://mersenne.org/M188416717[/url] [url]https://mersenne.org/M188422349[/url] [url]https://mersenne.org/M188423111[/url] [url]https://mersenne.org/M188424043[/url] [url]https://mersenne.org/M188516227[/url] [url]https://mersenne.org/M188603507[/url] [url]https://mersenne.org/M188644829[/url] [url]https://mersenne.org/M188659091[/url] [url]https://mersenne.org/M188661097[/url] [url]https://mersenne.org/M189342383[/url] [url]https://mersenne.org/M191135237[/url] [url]https://mersenne.org/M191138693[/url] [url]https://mersenne.org/M191146519[/url] [url]https://mersenne.org/M191148143[/url] [url]https://mersenne.org/M191154797[/url] [url]https://mersenne.org/M191199653[/url] [url]https://mersenne.org/M191202373[/url] [url]https://mersenne.org/M191206313[/url] [url]https://mersenne.org/M191212421[/url] [url]https://mersenne.org/M191214061[/url] [url]https://mersenne.org/M191272363[/url] [url]https://mersenne.org/M191280917[/url] [url]https://mersenne.org/M191283707[/url] [url]https://mersenne.org/M191284139[/url] [url]https://mersenne.org/M191284193[/url] [url]https://mersenne.org/M191284631[/url] [url]https://mersenne.org/M191285009[/url] [url]https://mersenne.org/M191289121[/url] [url]https://mersenne.org/M191289379[/url] [url]https://mersenne.org/M191298493[/url] [url]https://mersenne.org/M201365377[/url] [url]https://mersenne.org/M204431377[/url] [url]https://mersenne.org/M209968169[/url] [url]https://mersenne.org/M212867069[/url] [url]https://mersenne.org/M216635219[/url] [url]https://mersenne.org/M233579849[/url] [url]https://mersenne.org/M235452367[/url] [url]https://mersenne.org/M235558781[/url] [url]https://mersenne.org/M236951137[/url] [url]https://mersenne.org/M238521893[/url] [url]https://mersenne.org/M240874213[/url] [url]https://mersenne.org/M241518769[/url] [url]https://mersenne.org/M242491463[/url] [url]https://mersenne.org/M243069601[/url] [url]https://mersenne.org/M243858817[/url] [url]https://mersenne.org/M246439639[/url] [url]https://mersenne.org/M247314493[/url] [url]https://mersenne.org/M248083733[/url] [url]https://mersenne.org/M248744597[/url] [url]https://mersenne.org/M252202289[/url] [url]https://mersenne.org/M257744387[/url] [url]https://mersenne.org/M258027433[/url] [url]https://mersenne.org/M258230057[/url] [url]https://mersenne.org/M259223183[/url] [url]https://mersenne.org/M259711303[/url] [url]https://mersenne.org/M261399217[/url] [url]https://mersenne.org/M261600821[/url] [url]https://mersenne.org/M262347751[/url] [url]https://mersenne.org/M262371673[/url] [url]https://mersenne.org/M262932017[/url] [url]https://mersenne.org/M263487907[/url] [url]https://mersenne.org/M264306487[/url] [url]https://mersenne.org/M264406711[/url] [url]https://mersenne.org/M264483083[/url] [url]https://mersenne.org/M264728713[/url] [url]https://mersenne.org/M264750253[/url] [url]https://mersenne.org/M265111681[/url] [url]https://mersenne.org/M265204549[/url] [url]https://mersenne.org/M265278163[/url] [url]https://mersenne.org/M265299017[/url] [url]https://mersenne.org/M265409411[/url] [url]https://mersenne.org/M265463221[/url] [url]https://mersenne.org/M265475671[/url] [url]https://mersenne.org/M265670557[/url] [url]https://mersenne.org/M265791527[/url] [url]https://mersenne.org/M265832731[/url] [url]https://mersenne.org/M265841143[/url] [url]https://mersenne.org/M266031251[/url] [url]https://mersenne.org/M266036299[/url] [url]https://mersenne.org/M266065001[/url] [url]https://mersenne.org/M266098873[/url] 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[url]https://mersenne.org/M925251517[/url] [url]https://mersenne.org/M925918793[/url] [url]https://mersenne.org/M926214629[/url] [url]https://mersenne.org/M929794609[/url] [url]https://mersenne.org/M930594649[/url] [url]https://mersenne.org/M930919037[/url] [url]https://mersenne.org/M931376821[/url] [url]https://mersenne.org/M936759839[/url] [url]https://mersenne.org/M938647001[/url] [url]https://mersenne.org/M944011273[/url] [url]https://mersenne.org/M946310231[/url] [url]https://mersenne.org/M948777979[/url] [url]https://mersenne.org/M951404147[/url] [url]https://mersenne.org/M956443429[/url] [url]https://mersenne.org/M960585911[/url] [url]https://mersenne.org/M961755293[/url] [url]https://mersenne.org/M963535717[/url] [url]https://mersenne.org/M965364979[/url] [url]https://mersenne.org/M971859341[/url] [url]https://mersenne.org/M972272659[/url] [url]https://mersenne.org/M973750237[/url] [url]https://mersenne.org/M973962911[/url] [url]https://mersenne.org/M977189299[/url] [url]https://mersenne.org/M981847247[/url] [url]https://mersenne.org/M983648077[/url] [url]https://mersenne.org/M986943829[/url] [url]https://mersenne.org/M990843277[/url] [url]https://mersenne.org/M991185421[/url] [url]https://mersenne.org/M993797821[/url] [url]https://mersenne.org/M994713887[/url] [url]https://mersenne.org/M994913209[/url] [url]https://mersenne.org/M995117147[/url] [url]https://mersenne.org/M996024301[/url] [url]https://mersenne.org/M996126983[/url] [url]https://mersenne.org/M997690357[/url] [url]https://mersenne.org/M997732003[/url] [url]https://mersenne.org/M998961239[/url][/CODE] Trial factoring, GPU? (8 exponents:) [CODE] [url]https://mersenne.org/M99043661[/URL] [url]https://mersenne.org/M101963839[/URL] [url]https://mersenne.org/M102084947[/URL] [url]https://mersenne.org/M103258193[/URL] [url]https://mersenne.org/M104410819[/URL] [url]https://mersenne.org/M107038147[/URL] [url]https://mersenne.org/M107160121[/URL] [url]https://mersenne.org/M107163127[/URL] [/CODE] |
ECM (207 exponents):
[CODE][url]https://mersenne.org/M562997[/url] [url]https://mersenne.org/M565387[/url] [url]https://mersenne.org/M568171[/url] [url]https://mersenne.org/M568643[/url] [url]https://mersenne.org/M574181[/url] [url]https://mersenne.org/M576151[/url] [url]https://mersenne.org/M582761[/url] [url]https://mersenne.org/M583577[/url] [url]https://mersenne.org/M584693[/url] [url]https://mersenne.org/M585727[/url] [url]https://mersenne.org/M592337[/url] [url]https://mersenne.org/M599843[/url] [url]https://mersenne.org/M612349[/url] [url]https://mersenne.org/M617767[/url] [url]https://mersenne.org/M622513[/url] [url]https://mersenne.org/M624917[/url] [url]https://mersenne.org/M627791[/url] [url]https://mersenne.org/M633767[/url] [url]https://mersenne.org/M635363[/url] [url]https://mersenne.org/M635939[/url] [url]https://mersenne.org/M641873[/url] [url]https://mersenne.org/M643567[/url] [url]https://mersenne.org/M645737[/url] [url]https://mersenne.org/M648289[/url] 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[url]https://mersenne.org/M1152589[/url] [url]https://mersenne.org/M1156769[/url] [url]https://mersenne.org/M1158551[/url] [url]https://mersenne.org/M1158613[/url] [url]https://mersenne.org/M1158823[/url] [url]https://mersenne.org/M1160459[/url] [url]https://mersenne.org/M1160513[/url] [url]https://mersenne.org/M1162321[/url] [url]https://mersenne.org/M1162691[/url] [url]https://mersenne.org/M1162937[/url] [url]https://mersenne.org/M1165873[/url] [url]https://mersenne.org/M1169281[/url] [url]https://mersenne.org/M1170109[/url] [url]https://mersenne.org/M1170317[/url] [url]https://mersenne.org/M1172009[/url] [url]https://mersenne.org/M1174337[/url] [url]https://mersenne.org/M1176173[/url] [url]https://mersenne.org/M1176397[/url] [url]https://mersenne.org/M1177489[/url] [url]https://mersenne.org/M1177739[/url] [url]https://mersenne.org/M1179859[/url] [url]https://mersenne.org/M1180027[/url] [url]https://mersenne.org/M1180447[/url] [url]https://mersenne.org/M1180771[/url] [url]https://mersenne.org/M1182121[/url] [url]https://mersenne.org/M1183771[/url] [url]https://mersenne.org/M1187287[/url] [url]https://mersenne.org/M1188689[/url] [url]https://mersenne.org/M1188731[/url] [url]https://mersenne.org/M1189171[/url] [url]https://mersenne.org/M1190429[/url] [url]https://mersenne.org/M1190639[/url] [url]https://mersenne.org/M1192183[/url] [url]https://mersenne.org/M1192753[/url] [url]https://mersenne.org/M1220029[/url] [url]https://mersenne.org/M1220077[/url] [url]https://mersenne.org/M2440943[/url] [/CODE] |
[QUOTE=henryzz;468494]You sound like RDS[/QUOTE]
Unlike RDS, he stuck to math and facts. |
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