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2008-01-01, 03:37
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#1 |
Nov 2003
1110001001102 Posts |
k*2^n-1 primes in 2007
Here is the list of 100 largest known primes of form k*2^n-1, k>=3 at the end of 2007. Based on the Top-5000 list maintained by prof. Caldwell.
Ranking: r1, rank among k*2^n-1, k>=3 r2, rank among all known primes Code:
------------------------------------------------------------------------- r1 r2 description digits who year comment ------------------------------------------------------------------------- 1 13 938237*2^3752950-1 1129757 L521 2007 Woodall 2 15 3*2^3136255-1 944108 L256 2007 3 22 342673*2^2639439-1 794556 L53 2007 4 25 26773*2^2465343-1 742147 L197 2006 5 26 737*2^2382804-1 717299 L191 2007 6 27 1183953*2^2367907-1 712818 L447 2007 Woodall 7 28 275293*2^2335007-1 702913 L193 2006 8 29 3*2^2312734-1 696203 L158 2005 9 30 450457*2^2307905-1 694755 L172 2006 10 33 114487*2^2198389-1 661787 L179 2006 11 34 196597*2^2178109-1 655682 L175 2006 12 39 121*2^2033941-1 612280 L162 2006 13 40 251749*2^2013995-1 606279 L436 2007 Woodall 14 41 467917*2^1993429-1 600088 L160 2005 15 42 137137*2^1993201-1 600019 L321 2007 16 44 121*2^1954243-1 588288 L162 2006 17 46 345067*2^1876573-1 564911 g59 2005 18 48 137*2^1849238-1 556679 L321 2007 19 51 417643*2^1800787-1 542097 L134 2005 20 52 357659*2^1779748-1 535764 L47 2005 21 54 253*2^1722623-1 518564 L145 2007 rps 22 55 121*2^1695499-1 510399 L62 2005 23 58 469949*2^1649228-1 496473 L160 2007 24 61 58753*2^1594323-1 479944 p190 2006 25 62 737*2^1592724-1 479461 L191 2006 26 63 110413*2^1591999-1 479245 L111 2005 27 65 121*2^1589157-1 478387 L65 2005 28 72 234847*2^1535589-1 462264 L73 2005 29 73 121*2^1526097-1 459404 L65 2005 30 76 2232007*2^1490605-1 448724 L4 2003 31 77 29*2^1478344-1 445028 L10 2005 32 79 325627*2^1472117-1 443157 L111 2005 33 80 1467763*2^1467763-1 441847 L381 2007 Woodall 34 81 77*2^1467554-1 441780 L145 2006 rps 35 85 149797*2^1414137-1 425703 L105 2005 36 87 192089*2^1395688-1 420150 L49 2004 37 95 15*2^1344313-1 404680 L139 2007 rps 38 109 138847*2^1283793-1 386466 L2 2003 39 112 1268979*2^1268979-1 382007 L201 2007 Woodall 40 114 11*2^1261478-1 379744 L163 2006 rps 41 116 26869*2^1257787-1 378637 L466 2007 42 119 80857169*2^1251076-1 376620 L10 2004 43 126 3*2^1232255-1 370947 L30 2004 44 132 3*2^1201046-1 361552 L77 2004 45 133 502541*2^1199930-1 361221 L93 2004 46 134 1195203*2^1195203-1 359799 L124 2005 Woodall 47 137 71009*2^1185112-1 356760 L47 2004 48 139 617*2^1175468-1 353854 L426 2007 rps 49 142 152713*2^1154707-1 347607 g23 2004 50 145 350107*2^1144101-1 344415 L35 2004 51 146 209826493*2^1140855-1 343440 L10 2004 52 147 500621*2^1138518-1 342734 L73 2004 53 148 504613*2^1136459-1 342114 L84 2004 54 154 99*2^1106989-1 333239 L486 2007 rps 55 155 11*2^1104606-1 332521 L10 2005 56 157 289*2^1098117-1 330569 L6 2006 57 160 412717*2^1084409-1 326446 L76 2004 58 161 15*2^1084010-1 326321 L139 2006 rps 59 162 150847*2^1076441-1 324047 L73 2004 60 164 209826493*2^1071303-1 322503 L10 2004 61 165 2203*2^1069647-1 322000 L123 2006 62 166 864316301*2^1055106-1 317628 L426 2007 rps 63 168 11*2^1044086-1 314303 L10 2005 64 169 151515*2^1043018-1 313985 L426 2007 rps 65 171 121*2^1039965-1 313063 L65 2004 66 173 85*2^1034069-1 311288 L323 2007 rps 67 178 6119*2^1011416-1 304471 L251 2007 rps 68 179 9*2^1010277-1 304125 L80 2007 69 188 21*2^999599-1 300911 L56 2005 70 190 1515*2^996848-1 300085 L200 2007 rps 71 191 351351*2^996709-1 300045 L80 2006 72 193 3*2^992700-1 298833 L59 2004 73 195 121*2^990219-1 298088 L66 2004 74 196 21*2^986130-1 296857 L56 2005 75 197 137137*2^978229-1 294482 L321 2007 76 198 69*2^978209-1 294473 L260 2007 rps 77 204 111*2^959671-1 288892 L282 2007 rps 78 205 231*2^959375-1 288804 L138 2006 rps 79 206 1515*2^955219-1 287553 L200 2007 rps 80 207 247*2^952069-1 286604 L138 2006 rps 81 209 12345*2^948054-1 285397 L200 2007 rps 82 210 87*2^942790-1 283811 L145 2006 rps 83 211 25*2^942563-1 283742 L183 2006 rps 84 213 246419198025*2^935249-1 281550 L106 2007 85 216 243163663*2^919087-1 276682 L10 2004 86 217 125*2^918494-1 276497 L384 2007 rps 87 219 19*2^916763-1 275975 L177 2007 rps 88 220 737*2^906168-1 272787 L191 2006 89 223 15*2^902474-1 271673 L52 2006 90 224 309817*2^901173-1 271286 L64 2004 91 225 101*2^900358-1 271037 L183 2006 rps 92 227 19581121*2^893547-1 268992 p49 2004 93 229 2995125705*2^891645-1 268422 L145 2006 rps 94 233 5077*2^881829-1 265461 L251 2007 rps 95 238 69*2^867653-1 261192 L138 2006 rps 96 239 170591*2^866870-1 260960 L47 2004 97 240 3234846615*2^865933-1 260682 p113 2007 98 241 93997*2^864401-1 260216 L49 2004 99 242 19581121*2^862127-1 259534 p49 2003 100 243 2013289*2^859433-1 258722 L466 2007 ------------------------------------------------------------------------- 33 found in 2007. Happy New Year! |
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2008-01-01, 03:43
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#2 |
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Nov 2003
2·1,811 Posts |
k*2^n-1 primes found in 2007
Here is the list of 100 largest primes of form k*2^n-1, k>=3 found in 2007. Based on the Top-5000 list maintained by prof. Caldwell.
Ranking: r1, rank among k*2^n-1, k>=3 r2, rank among all known primes Code:
--------------------------------------------------------------- r1 r2 description digits who comment --------------------------------------------------------------- 1 13 938237*2^3752950-1 1129757 L521 Woodall 2 15 3*2^3136255-1 944108 L256 3 22 342673*2^2639439-1 794556 L53 4 26 737*2^2382804-1 717299 L191 5 27 1183953*2^2367907-1 712818 L447 Woodall 6 40 251749*2^2013995-1 606279 L436 Woodall 7 42 137137*2^1993201-1 600019 L321 8 48 137*2^1849238-1 556679 L321 9 54 253*2^1722623-1 518564 L145 rps 10 58 469949*2^1649228-1 496473 L160 11 80 1467763*2^1467763-1 441847 L381 Woodall 12 95 15*2^1344313-1 404680 L139 rps 13 112 1268979*2^1268979-1 382007 L201 Woodall 14 116 26869*2^1257787-1 378637 L466 15 139 617*2^1175468-1 353854 L426 rps 16 154 99*2^1106989-1 333239 L486 rps 17 166 864316301*2^1055106-1 317628 L426 rps 18 169 151515*2^1043018-1 313985 L426 rps 19 173 85*2^1034069-1 311288 L323 rps 20 178 6119*2^1011416-1 304471 L251 rps 21 179 9*2^1010277-1 304125 L80 22 190 1515*2^996848-1 300085 L200 rps 23 197 137137*2^978229-1 294482 L321 24 198 69*2^978209-1 294473 L260 rps 25 204 111*2^959671-1 288892 L282 rps 26 206 1515*2^955219-1 287553 L200 rps 27 209 12345*2^948054-1 285397 L200 rps 28 213 246419198025*2^935249-1 281550 L106 29 217 125*2^918494-1 276497 L384 rps 30 219 19*2^916763-1 275975 L177 rps 31 233 5077*2^881829-1 265461 L251 rps 32 240 3234846615*2^865933-1 260682 p113 33 243 2013289*2^859433-1 258722 L466 34 244 1486245*2^859433-1 258722 L466 35 245 1283911*2^859433-1 258722 L466 36 251 83*2^851092-1 256207 L80 37 252 261*2^850383-1 255994 L478 rps 38 255 51*2^845494-1 254521 L80 39 257 201*2^840735-1 253089 L282 rps 40 258 57*2^839446-1 252701 L80 41 259 35*2^839082-1 252591 L325 rps 42 263 117*2^834916-1 251337 L261 rps 43 265 51*2^832630-1 250649 L80 44 266 291*2^832410-1 250583 L261 rps 45 267 237*2^832053-1 250476 L261 rps 46 271 173*2^828808-1 249499 L145 rps 47 273 261*2^827599-1 249135 L261 rps 48 275 197*2^825188-1 248409 L282 rps 49 277 181*2^823853-1 248007 L138 rps 50 282 45*2^818648-1 246440 L282 rps 51 283 75*2^814857-1 245299 L80 52 284 105*2^814850-1 245297 L384 rps 53 287 291*2^810347-1 243942 L421 rps 54 290 35*2^805222-1 242398 L142 rps 55 292 261*2^802123-1 241466 L261 rps 56 293 105*2^801978-1 241422 L384 rps 57 308 201*2^799611-1 240710 L282 rps 58 311 3645*2^792240-1 238492 L261 rps 59 312 111*2^791502-1 238268 L282 rps 60 318 285*2^780300-1 234897 L425 rps 61 320 246419198025*2^778905-1 234486 L106 62 324 7003141*2^777777-1 234142 L81 63 325 6982195*2^777777-1 234142 L81 64 326 6870877*2^777777-1 234142 L81 65 327 6655117*2^777777-1 234142 L81 66 328 5901565*2^777777-1 234141 L81 67 338 201*2^775453-1 233437 L282 rps 68 339 22183*2^773447-1 232836 L251 rps 69 340 31*2^773227-1 232767 L330 rps 70 341 33*2^773030-1 232707 L488 rps 71 347 213*2^760942-1 229069 L261 rps 72 348 51127*2^759513-1 228641 L83 73 349 246419198025*2^757961-1 228181 L106 74 350 1391281*2^756839-1 227838 L466 75 351 1334079*2^756839-1 227838 L466 76 352 1081255*2^756839-1 227838 L466 77 353 755061*2^756839-1 227838 L466 78 357 736320585*2^753905-1 226957 L200 rps 79 358 246419198025*2^752612-1 226571 L106 80 368 273*2^742930-1 223647 L323 rps 81 369 151515*2^742445-1 223504 L200 rps 82 371 81*2^741917-1 223342 L268 rps 83 379 237*2^729654-1 219651 L261 rps 84 384 137137*2^725437-1 218384 L321 85 394 91*2^711335-1 214136 L323 rps 86 396 213*2^709727-1 213652 L261 rps 87 399 57*2^707245-1 212904 L384 rps 88 402 151515*2^705873-1 212495 L200 rps 89 404 267*2^705028-1 212238 L260 rps 90 406 7331*2^704842-1 212183 L251 rps 91 416 24067*2^700073-1 210748 L251 rps 92 417 6215657*2^700000-1 210728 L81 93 418 4786305*2^700000-1 210728 L81 94 419 4649865*2^700000-1 210728 L81 95 422 2758665*2^700000-1 210728 L81 96 424 2500883*2^700000-1 210728 L81 97 434 117*2^697458-1 209958 L261 rps 98 436 6794935*2^696969-1 209816 L81 99 437 6145851*2^696969-1 209816 L81 100 438 4549431*2^696969-1 209816 L81 --------------------------------------------------------------- The lists at the end of 2006 can be found here. |
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