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2019-04-18, 07:36
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#12 |
Feb 2003
27·3·5 Posts |
Here are the extensions to ATH's results up to k=1000B (=1e12):
Consecutive first occurrence gaps 1359 up to 1635, and nonconsecutive first occurrence gaps up to 2377. The extensions to the maximal gap list are given below. Code:
gap k 1359 238021889388 1360 120701590522 1361 103656076897 1362 129780127055 1363 45464706810 1364 236116004983 1365 27432631065 1366 221323766702 1367 66664704428 1368 79675959260 1369 105795508798 1370 22751684835 1371 150422884902 1372 73987959848 1373 91101657665 1374 74619205678 1375 106433204497 1376 109109662112 1377 140926519020 1378 158222902962 1379 59513006413 1380 83535481318 1381 81120569787 1382 208297454633 1383 82037154155 1384 91105669713 1385 35954269187 1386 36654125322 1387 82436707565 1388 52106714982 1389 335699670478 1390 134783026287 1391 91527303572 1392 160241217295 1393 78441568602 1394 107218832948 1395 93204583073 1396 370369427962 1397 71529209675 1398 89717150497 1399 167763335213 1400 78769799252 1401 113406055667 1402 83591984703 1403 209318000600 1404 115946907303 1405 60066856568 1406 157757582267 1407 207000817860 1408 75688827280 1409 131711929323 1410 199574686315 1411 48278160327 1412 157757709578 1413 32135929095 1414 179075794238 1415 49037845735 1416 64167955752 1417 117577979190 1418 108513597027 1419 77078300443 1420 74951308542 1421 42119304362 1422 101735004478 1423 142152878497 1424 258224787443 1425 88942037140 1426 114261540757 1427 228073106628 1428 100389566412 1429 175835907578 1430 48978765967 1431 105371512887 1432 89851341625 1433 211777215930 1434 197709087693 1435 110562730142 1436 34440671017 1437 141185526520 1438 167850568830 1439 94595234198 1440 34516209527 1441 195969981917 1442 136888972125 1443 134581666552 1444 159728123338 1445 38840382823 1446 227253338462 1447 57301290370 1448 77920988750 1449 102332614223 1450 108516370937 1451 64095115322 1452 151527991675 1453 145272707550 1454 174799142838 1455 81631078743 1456 195778814802 1457 301410421995 1458 264657155665 1459 206268027728 1460 64584093742 1461 472019855132 1462 88475830910 1463 69741598787 1464 224994765053 1465 135767046975 1466 275157656942 1467 85661945075 1468 63139736062 1469 228677692513 1470 106208976653 1471 156171984272 1472 138299223690 1473 184783689402 1474 365110475063 1475 67410836280 1476 267918092432 1477 185821439738 1478 96139203857 1479 214041248743 1480 240784621312 1481 228476499377 1482 176427443750 1483 48773094382 1484 136319467498 1485 169809420105 1486 150516739082 1487 405178602348 1488 209618644275 1489 130741136258 1490 88340661855 1491 227858144272 1492 121639858400 1493 66924164457 1494 406142933448 1495 69782047618 1496 174973906777 1497 291869230735 1498 308394175852 1499 22339570278 1500 172823544343 1501 326074608547 1502 128837925765 1503 181674927455 1504 289506845778 1505 160823433270 1506 227491883602 1507 176020578323 1508 279911847660 1509 434412984948 1510 163775464003 1511 393469552312 1512 218349176503 1513 342721571537 1514 440909475828 1515 155390806498 1516 85283577452 1517 196413282468 1518 184159612907 1519 235557862248 1520 159460255028 1521 359489269902 1522 219322573465 1523 147488057610 1524 263159931988 1525 98616660978 1526 56105289977 1527 194013931730 1528 263122426457 1529 137914593968 1530 164942161335 1531 82643395422 1532 238243169945 1533 247333123902 1534 450299367998 1535 328710671530 1536 151913191462 1537 343278293043 1538 119496454527 1539 225373027793 1540 139666887840 1541 251898401212 1542 181392272663 1543 180056667807 1544 146578135928 1545 70464152903 1546 168996745347 1547 160429275275 1548 142976782372 1549 170014476063 1550 174553795390 1551 222454633082 1552 33051947625 1553 37182176622 1554 344855543718 1555 119208146283 1556 107282165062 1557 143282458305 1558 164872223950 1559 385122746008 1560 62578713270 1561 176158811742 1562 118027566675 1563 364921287610 1564 299852086093 1565 136243056022 1566 399858131992 1567 223700692605 1568 359606250350 1569 558397733113 1570 206516426483 1571 281055726357 1572 215157908388 1573 248533440965 1574 605483702178 1575 103750795712 1576 278322616602 1577 185624758875 1578 354907107055 1579 275064432933 1580 184298726117 1581 513934851092 1582 383060493443 1583 129919858890 1584 550087135293 1585 96643867775 1586 244777442157 1587 144666194755 1588 317882759267 1589 504467037198 1590 116320889387 1591 552495066182 1592 385287103058 1593 307663309660 1594 268309573438 1595 177702480225 1596 255548544727 1597 785707760883 1598 276185251937 1599 310000481863 1600 243015237435 1601 476094473867 1602 401584755318 1603 121584681445 1604 333819870513 1605 185545828858 1606 809203672447 1607 220818051338 1608 562941500147 1609 566988071438 1610 109354338662 1611 538043378982 1612 383806176040 1613 128518326722 1614 425743230153 1615 210586309103 1616 601754613962 1617 211557516208 1618 151521188780 1619 261923049103 1620 111423209912 1621 466752047347 1622 395629846073 1623 284209749890 1624 201089339318 1625 297772201955 1626 354443118657 1627 538605605153 1628 563886417640 1629 450374566348 1630 280475819957 1631 117959421867 1632 256713987023 1633 103293294022 1634 432495163513 1635 101323871015 1637 314387243880 1638 223187612730 1639 430370370398 1640 251399472527 1641 272511992827 1642 212024898078 1643 158850706422 1645 464373757405 1646 197557993677 1647 384183995148 1648 555439323975 1649 158176828393 1650 409316753062 1651 312158180092 1652 470531332488 1653 841664786197 1654 701771647838 1655 405384059735 1656 514927351307 1657 229220533173 1658 166226961612 1659 165136905488 1660 133864375453 1661 633288781027 1662 256117920503 1663 492030454557 1664 131415761768 1665 291876048707 1666 802227020182 1667 375860209433 1668 285028014162 1669 859713724753 1670 295839732305 1671 579035340417 1672 161263436148 1673 498618428432 1674 636283516158 1675 616638723823 1676 859939543782 1677 508171256813 1678 487863089385 1679 600200255728 1680 448760176352 1681 569028734977 1682 280877509220 1684 435854938013 1685 256321846760 1687 156290145345 1688 611197905670 1689 984424116398 1690 652938228583 1691 463542106657 1692 254281560703 1693 431955803822 1694 334135265893 1695 282763122140 1696 450016651352 1697 822643098295 1698 565141146050 1699 372837607753 1700 58917239540 1701 433407295157 1702 298348323303 1703 466812660410 1705 517453687215 1706 772867305887 1707 524920422073 1708 459952950865 1709 515336777288 1710 89470349442 1712 567801655963 1713 216733386980 1715 555007406300 1716 485816451332 1717 504463536573 1718 661561148110 1719 325264034063 1720 453489992522 1722 610655512490 1723 80799633875 1724 634233966553 1725 762318092370 1726 261705340277 1727 225881516975 1728 538335755667 1729 806506374413 1730 217895151387 1731 707703825092 1732 735596463515 1733 768450016780 1734 745631868578 1735 356177753412 1736 741222736422 1737 761250576468 1738 671721527412 1740 384364766532 1741 563317414062 1742 724809604908 1743 370979739580 1744 359521940948 1745 300186232845 1746 447197130142 1747 907203956603 1748 528077281142 1749 801659775458 1750 280488680647 1751 739849772267 1752 496386470473 1753 714960674750 1754 338841041033 1755 532001966893 1756 671605907382 1757 294509651840 1759 298338286438 1761 584390565997 1762 318182662973 1763 600635385640 1764 240121693893 1766 473256996777 1767 828485975438 1769 782711361523 1770 855953593323 1771 988638208437 1772 655550748640 1773 411932055292 1774 447362234533 1775 449770326922 1776 805225566947 1777 550358556340 1778 106405396032 1780 982232544190 1781 841171099652 1785 130744752537 1786 825384984377 1787 776268942683 1788 854615602792 1789 646099785688 1790 557950608758 1791 369489065347 1792 689680764418 1794 621462178578 1795 750466894258 1797 582262097498 1798 608219715197 1799 244370452833 1800 831467803302 1802 800163087448 1806 363596492507 1807 589681107438 1808 374311870175 1810 133135498198 1811 754512505717 1815 169866686215 1816 536707956407 1817 956610710023 1818 707849433580 1819 478026230448 1820 524708956392 1822 363792713305 1823 393901596172 1825 718703397508 1827 514690190788 1828 544205194130 1830 283716126022 1832 746075980130 1836 663607308612 1837 361289615670 1838 284106487357 1840 389453919375 1841 738549390442 1843 737313907580 1846 823245280032 1847 675857800098 1848 723741177537 1850 804839675663 1851 363074768532 1853 932204536545 1857 729575524785 1860 843314053692 1862 663487911713 1863 336185917595 1865 781793275960 1866 892852657037 1870 513194527407 1871 971781746092 1872 447811616018 1874 750393104603 1875 598433097470 1880 904212211453 1881 781557375732 1885 676152407723 1887 426285083663 1890 151287342070 1892 201865544225 1893 290614184492 1895 854745621275 1897 359738661993 1898 132437316545 1900 619983477157 1901 635700745862 1903 675525244735 1905 932239203395 1912 804438922933 1915 470420475572 1918 804794472115 1925 523274691888 1926 696620005307 1932 960136903043 1935 664808242868 1936 279967183457 1937 642270715125 1950 982578277387 1953 954508482785 1955 511426336883 1958 757895739535 1968 652547157105 1971 824751367527 1979 614991456963 1984 564720846228 1986 944675774037 1987 645901356965 1994 721147884418 1997 207741061965 2006 541952390642 2016 389348710292 2023 224142765215 2029 548899132323 2032 801995327063 2048 249479281077 2072 461157712565 2073 902743525100 2074 646834943323 2080 665814402872 2086 518189243667 2090 524000762887 2093 362104284385 2096 654588515312 2105 359442044602 2163 509866874615 2175 405935625685 2183 823397649847 2228 986150450957 2377 748572833888 Code:
maxgap k 1997 207741061965 2023 224142765215 2048 249479281077 2105 359442044602 2175 405935625685 2377 748572833888 |
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2019-04-20, 14:07
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#13 |
May 2018
11816 Posts |
114587 is followed by two consecutive record gaps of 155 and 168. The next two numbers in the sequence are 114742 and 114910. This corresponds to the twin primes (687521, 687523), (688451, 688453), and (689459, 689461).
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2019-04-25, 17:47
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#14 |
Jun 2003
Suva, Fiji
23·3·5·17 Posts |
I thought I would start at 1e15 to make sure of no overlaps. In a couple of hours I am at 1.011e15 and have found candidates for all up to k= 2138 and many others up to k=2928.
Here's the perl code I am using - it takes advantage of danaj's fast forprimes function Code:
#!/usr/bin/env perl
use warnings;
use strict;
use Math::GMPz;
use Math::BigFloat lib=>"GMP";
use Math::Prime::Util qw/:all/;
use v5.10;
$|=1;
my $interval = 1_000_000_000;
my $overlap = 5_000;
my $numberofiterations = 5_000;
my $from = 1_001_150_000_005_000+5_000;
my @twins;
my $mingap = 2_138;
for (my $k=0; $k <= $numberofiterations; $k++)
{
my $range = $from+$k*$interval;
my $start = $range-$overlap;
my $end = $range+$interval+$overlap;
my @twins;
forprimes
{
if (is_prime($_+2)) {push @twins,$_;}
}$start,$end;
say "# of twins= ",scalar(@twins), " in the range: ", $start," ",$end;
for (my $l=1; $l <= scalar(@twins)-1; $l++)
{
my $gap = ($twins[$l]-$twins[$l-1])/6;
my $first = ($twins[$l-1]+1)/6;
my $second = ($twins[$l]+1)/6;
if ($gap >= $mingap) {say $gap, " ", $first;}
}
}
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2019-04-26, 07:49
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#15 | |
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Jun 2003
Suva, Fiji
23×3×5×17 Posts |
Quote:
I've started two other runs at 1.1e15 and 1.2e15 |
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2019-04-27, 14:16
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#16 |
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Jun 2003
Suva, Fiji
23·3·5·17 Posts |
I'm also reserving 1e12 to 1e15.
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2019-04-28, 08:26
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#17 | |
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Jun 2003
Suva, Fiji
23·3·5·17 Posts |
Quote:
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2019-04-29, 09:37
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#18 |
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Jun 2003
Suva, Fiji
204010 Posts |
Here is the table of consecutive first instance gaps between twin primes as of this morning
Code:
1 1 rudy235 2 3 rudy235 3 7 rudy235 4 103 rudy235 5 12 rudy235 6 52 rudy235 7 378 ATH 8 87 rudy235 9 313 rudy235 10 77 rudy235 11 287 rudy235 12 58 rudy235 13 192 rudy235 14 298 rudy235 15 597 ATH 16 357 rudy235 17 1075 rudy235 18 220 rudy235 19 3563 ATH 20 248 rudy235 21 2042 ATH 22 800 ATH 23 147 rudy235 24 3843 ATH 25 110 rudy235 26 3257 ATH 27 2063 ATH 28 397 ATH 29 6458 ATH 30 1755 ATH 31 6227 ATH 32 1438 ATH 33 1507 ATH 34 5638 ATH 35 980 ATH 36 13372 ATH 37 2560 ATH 38 7637 ATH 39 6018 ATH 40 2438 ATH 41 6332 ATH 42 6088 ATH 43 14542 ATH 44 11833 ATH 45 2478 ATH 46 6692 ATH 47 2233 ATH 48 9105 ATH 49 6808 ATH 50 8432 ATH 51 23277 ATH 52 7968 ATH 53 6585 ATH 54 23133 ATH 55 13815 ATH 56 25347 ATH 57 13953 ATH 58 7462 ATH 59 35798 ATH 60 31972 ATH 61 25587 ATH 62 3090 ATH 63 17475 ATH 64 90423 ATH 65 9002 ATH 66 72942 ATH 67 19033 ATH 68 17850 ATH 69 32378 ATH 70 4377 ATH 71 12952 ATH 72 23693 ATH 73 48785 ATH 74 37058 ATH 75 14845 ATH 76 58077 ATH 77 35368 ATH 78 77697 ATH 79 18308 ATH 80 55143 ATH 81 33397 ATH 82 74400 ATH 83 4070 ATH 84 24168 ATH 85 20478 ATH 86 138187 ATH 87 80868 ATH 88 22890 ATH 89 56523 ATH 90 55632 ATH 91 37942 ATH 92 81448 ATH 93 44660 ATH 94 213103 ATH 95 97545 ATH 96 354662 ATH 97 27620 ATH 98 27977 ATH 99 383148 ATH 100 44905 ATH 101 125472 ATH 102 20013 ATH 103 76967 ATH 104 293123 ATH 105 10383 ATH 106 241847 ATH 107 91303 ATH 108 89567 ATH 109 91103 ATH 110 140420 ATH 111 129022 ATH 112 149863 ATH 113 130757 ATH 114 239678 ATH 115 126070 ATH 116 334862 ATH 117 100658 ATH 118 429182 ATH 119 304243 ATH 120 140795 ATH 121 614567 ATH 122 322018 ATH 123 199937 ATH 124 535353 ATH 125 73238 ATH 126 148897 ATH 127 135550 ATH 128 410312 ATH 129 217368 ATH 130 37355 ATH 131 264492 ATH 132 150433 ATH 133 187047 ATH 134 376973 ATH 135 500720 ATH 136 828307 ATH 137 156343 ATH 138 311532 ATH 139 767163 ATH 140 505115 ATH 141 569097 ATH 142 240345 ATH 143 41995 ATH 144 989058 ATH 145 116403 ATH 146 407412 ATH 147 308028 ATH 148 802070 ATH 149 989443 ATH 150 282408 ATH 151 707262 ATH 152 277258 ATH 153 234965 ATH 154 31318 ATH 155 114587 ATH 156 607952 ATH 157 292908 ATH 158 839762 ATH 159 410923 ATH 160 154445 ATH 161 518717 ATH 162 793900 ATH 163 526890 ATH 164 443443 ATH 165 437057 ATH 166 705787 ATH 167 632180 ATH 168 114742 ATH 169 1571558 ATH 170 1074442 ATH 171 2040992 ATH 172 799050 ATH 173 1042935 ATH 174 2320048 ATH 175 613727 ATH 176 322557 ATH 177 252443 ATH 178 1414700 ATH 179 1773728 ATH 180 302698 ATH 181 2253632 ATH 182 1038265 ATH 183 735717 ATH 184 1772778 ATH 185 608167 ATH 186 729092 ATH 187 364473 ATH 188 416322 ATH 189 3004313 ATH 190 2048442 ATH 191 880507 ATH 192 1052370 ATH 193 485555 ATH 194 1918663 ATH 195 857552 ATH 196 1402747 ATH 197 682880 ATH 198 1188775 ATH 199 2004258 ATH 200 340200 ATH 201 1511522 ATH 202 1678078 ATH 203 1335645 ATH 204 4055193 ATH 205 1722322 ATH 206 1372987 ATH 207 3142030 ATH 208 546497 ATH 209 543638 ATH 210 1330010 ATH 211 2007457 ATH 212 1338953 ATH 213 2109557 ATH 214 1627603 ATH 215 439318 ATH 216 4449232 ATH 217 901498 ATH 218 1416445 ATH 219 1886258 ATH 220 1793428 ATH 221 3411077 ATH 222 1580488 ATH 223 1720645 ATH 224 4460943 ATH 225 1982738 ATH 226 1974357 ATH 227 2670628 ATH 228 4723290 ATH 229 2574703 ATH 230 2635435 ATH 231 400027 ATH 232 2164430 ATH 233 1248642 ATH 234 6283358 ATH 235 6958413 ATH 236 3311417 ATH 237 8351255 ATH 238 1907630 ATH 239 8654928 ATH 240 924093 ATH 241 2998772 ATH 242 141725 ATH 243 1091750 ATH 244 3703248 ATH 245 749728 ATH 246 7232382 ATH 247 3165130 ATH 248 4443460 ATH 249 6222538 ATH 250 2463633 ATH 251 5315012 ATH 252 478160 ATH 253 4792547 ATH 254 4691848 ATH 255 811652 ATH 256 6088402 ATH 257 3515755 ATH 258 7532130 ATH 259 6281243 ATH 260 2195720 ATH 261 6950247 ATH 262 6548558 ATH 263 3503405 ATH 264 4290753 ATH 265 5494620 ATH 266 4225632 ATH 267 3418433 ATH 268 1974957 ATH 269 6039238 ATH 270 2331423 ATH 271 6206702 ATH 272 9813760 ATH 273 5335755 ATH 274 2450158 ATH 275 3031595 ATH 276 12364972 ATH 277 12908728 ATH 278 5582992 ATH 279 5159873 ATH 280 3796865 ATH 281 4553042 ATH 282 2046828 ATH 283 5461880 ATH 284 12514908 ATH 285 4172835 ATH 286 7935177 ATH 287 1653998 ATH 288 3934220 ATH 289 20158288 ATH 290 4158088 ATH 291 4820767 ATH 292 4105178 ATH 293 11322162 ATH 294 9113008 ATH 295 4135918 ATH 296 18194227 ATH 297 5011358 ATH 298 3960080 ATH 299 3129508 ATH 300 5232260 ATH 301 12167097 ATH 302 6988970 ATH 303 8117422 ATH 304 11951468 ATH 305 8106710 ATH 306 2681627 ATH 307 10473508 ATH 308 10340447 ATH 309 3210918 ATH 310 7666407 ATH 311 4619167 ATH 312 8278058 ATH 313 6400455 ATH 314 17187033 ATH 315 4702603 ATH 316 15209862 ATH 317 2442753 ATH 318 16896975 ATH 319 9072458 ATH 320 5301938 ATH 321 34220632 ATH 322 7522380 ATH 323 16858160 ATH 324 23102243 ATH 325 8320368 ATH 326 26359697 ATH 327 8442298 ATH 328 19084790 ATH 329 18287903 ATH 330 20969477 ATH 331 3583562 ATH 332 11808325 ATH 333 7186347 ATH 334 14821678 ATH 335 9228138 ATH 336 13069702 ATH 337 17811398 ATH 338 11018355 ATH 339 13511103 ATH 340 21878120 ATH 341 7581012 ATH 342 11702668 ATH 343 28398507 ATH 344 24668528 ATH 345 12763128 ATH 346 4961502 ATH 347 20779808 ATH 348 15215265 ATH 349 23685518 ATH 350 13793112 ATH 351 32928002 ATH 352 6521160 ATH 353 10293222 ATH 354 22956843 ATH 355 6302263 ATH 356 12593857 ATH 357 19960265 ATH 358 12270310 ATH 359 32898623 ATH 360 10196200 ATH 361 45449332 ATH 362 17042403 ATH 363 16624200 ATH 364 22301048 ATH 365 2897080 ATH 366 40950712 ATH 367 33111365 ATH 368 8149760 ATH 369 51585693 ATH 370 22896738 ATH 371 15476102 ATH 372 32159640 ATH 373 13446737 ATH 374 27670643 ATH 375 26215250 ATH 376 5125372 ATH 377 18111105 ATH 378 11993790 ATH 379 22279238 ATH 380 12127783 ATH 381 35827397 ATH 382 11787130 ATH 383 31053705 ATH 384 37896723 ATH 385 7089100 ATH 386 53895292 ATH 387 8877060 ATH 388 32429742 ATH 389 33247093 ATH 390 37801353 ATH 391 45403782 ATH 392 53265118 ATH 393 33932187 ATH 394 54592048 ATH 395 52420050 ATH 396 43802472 ATH 397 18049278 ATH 398 8268992 ATH 399 17798573 ATH 400 39051617 ATH 401 8438437 ATH 402 22831953 ATH 403 24129945 ATH 404 15630403 ATH 405 13404100 ATH 406 16157852 ATH 407 31911968 ATH 408 16036020 ATH 409 131974248 ATH 410 31893540 ATH 411 22425307 ATH 412 29484010 ATH 413 47602420 ATH 414 82119803 ATH 415 19775268 ATH 416 29386417 ATH 417 68602238 ATH 418 41778520 ATH 419 93495743 ATH 420 23842290 ATH 421 142202692 ATH 422 25123605 ATH 423 78731275 ATH 424 50655253 ATH 425 13855742 ATH 426 109107422 ATH 427 15573180 ATH 428 31192690 ATH 429 38107018 ATH 430 25165095 ATH 431 18371552 ATH 432 40731705 ATH 433 13834285 ATH 434 53527358 ATH 435 24080842 ATH 436 16710662 ATH 437 48520285 ATH 438 24629435 ATH 439 13132343 ATH 440 32978397 ATH 441 66760127 ATH 442 39234520 ATH 443 18875645 ATH 444 78330303 ATH 445 12612057 ATH 446 143010737 ATH 447 12373485 ATH 448 21431515 ATH 449 110247748 ATH 450 53824503 ATH 451 87678192 ATH 452 27733970 ATH 453 50006577 ATH 454 80319873 ATH 455 44847303 ATH 456 74767472 ATH 457 104140993 ATH 458 91272780 ATH 459 92708173 ATH 460 38535163 ATH 461 42691577 ATH 462 62031975 ATH 463 59148072 ATH 464 165948043 ATH 465 135221072 ATH 466 152264252 ATH 467 80953535 ATH 468 26303177 ATH 469 125150583 ATH 470 32932580 ATH 471 126663322 ATH 472 5470395 ATH 473 150927600 ATH 474 43090618 ATH 475 97938530 ATH 476 40838817 ATH 477 75363760 ATH 478 16149007 ATH 479 284804898 ATH 480 80309185 ATH 481 115470182 ATH 482 45943663 ATH 483 36014125 ATH 484 163951638 ATH 485 39471535 ATH 486 48453332 ATH 487 140964675 ATH 488 150869192 ATH 489 189444078 ATH 490 110206745 ATH 491 100964152 ATH 492 79923665 ATH 493 48026762 ATH 494 101611758 ATH 495 45163568 ATH 496 55908142 ATH 497 76410610 ATH 498 130733067 ATH 499 33934143 ATH 500 41429537 ATH 501 70253167 ATH 502 22713905 ATH 503 191574345 ATH 504 146498963 ATH 505 46437737 ATH 506 173190797 ATH 507 164960630 ATH 508 216902525 ATH 509 102749973 ATH 510 152688238 ATH 511 209690502 ATH 512 48815645 ATH 513 157862995 ATH 514 386570573 ATH 515 48852517 ATH 516 65749927 ATH 517 39161155 ATH 518 168549545 ATH 519 141866148 ATH 520 50182800 ATH 521 362098837 ATH 522 120656933 ATH 523 105170832 ATH 524 178905408 ATH 525 159979208 ATH 526 270179982 ATH 527 120056013 ATH 528 253317012 ATH 529 119288608 ATH 530 41440173 ATH 531 79966927 ATH 532 141871385 ATH 533 197378050 ATH 534 117206738 ATH 535 209633148 ATH 536 230621097 ATH 537 225768958 ATH 538 149105470 ATH 539 107503958 ATH 540 247994175 ATH 541 221250442 ATH 542 120739000 ATH 543 254478770 ATH 544 371148278 ATH 545 150743317 ATH 546 158681687 ATH 547 304231638 ATH 548 210201245 ATH 549 348848868 ATH 550 119082393 ATH 551 213351177 ATH 552 238235035 ATH 553 146988425 ATH 554 135184668 ATH 555 48778543 ATH 556 266472882 ATH 557 179175435 ATH 558 179486832 ATH 559 373649708 ATH 560 118767623 ATH 561 418105097 ATH 562 133244403 ATH 563 99186192 ATH 564 333303593 ATH 565 101807010 ATH 566 330170307 ATH 567 82334390 ATH 568 171665365 ATH 569 461913048 ATH 570 343740415 ATH 571 361007092 ATH 572 83969473 ATH 573 157917532 ATH 574 975992038 ATH 575 208413355 ATH 576 465571062 ATH 577 385601498 ATH 578 232052730 ATH 579 158837623 ATH 580 42658325 ATH 581 272912052 ATH 582 485700583 ATH 583 140274062 ATH 584 532220733 ATH 585 276236212 ATH 586 805665957 ATH 587 176958073 ATH 588 391344047 ATH 589 362709253 ATH 590 343599443 ATH 591 96230787 ATH 592 135656225 ATH 593 105832680 ATH 594 123912008 ATH 595 204503943 ATH 596 269491217 ATH 597 305953818 ATH 598 406283570 ATH 599 752414318 ATH 600 237903498 ATH 601 213329912 ATH 602 390995748 ATH 603 140998195 ATH 604 954806573 ATH 605 370473637 ATH 606 663391382 ATH 607 149046508 ATH 608 352775105 ATH 609 249857878 ATH 610 208120502 ATH 611 1000855662 ATH 612 417634343 ATH 613 552035622 ATH 614 345036853 ATH 615 242905400 ATH 616 141326852 ATH 617 810010058 ATH 618 688137917 ATH 619 271236933 ATH 620 193774213 ATH 621 136370567 ATH 622 257638638 ATH 623 319521510 ATH 624 250962968 ATH 625 559311310 ATH 626 1526295402 ATH 627 222255400 ATH 628 243023212 ATH 629 1207752558 ATH 630 173214632 ATH 631 985749397 ATH 632 337902708 ATH 633 250537490 ATH 634 65136288 ATH 635 404928923 ATH 636 538804067 ATH 637 178339938 ATH 638 275472495 ATH 639 696731203 ATH 640 421723087 ATH 641 1205491327 ATH 642 333242723 ATH 643 375536122 ATH 644 891125008 ATH 645 172730940 ATH 646 448706972 ATH 647 653288125 ATH 648 249183457 ATH 649 968771613 ATH 650 752190862 ATH 651 531453597 ATH 652 176380515 ATH 653 800990200 ATH 654 206795523 ATH 655 927234147 ATH 656 713470662 ATH 657 515432508 ATH 658 514294065 ATH 659 870602408 ATH 660 331622147 ATH 661 1020206457 ATH 662 171615535 ATH 663 455841750 ATH 664 931278113 ATH 665 282435977 ATH 666 2138760872 ATH 667 303122703 ATH 668 1051665225 ATH 669 897095818 ATH 670 929629507 ATH 671 373712582 ATH 672 571641690 ATH 673 521519827 ATH 674 1138708058 ATH 675 502328663 ATH 676 1058510057 ATH 677 1268768065 ATH 678 1185624415 ATH 679 445660388 ATH 680 393109768 ATH 681 672667072 ATH 682 440687683 ATH 683 856795660 ATH 684 1066747168 ATH 685 129325277 ATH 686 362174137 ATH 687 457057360 ATH 688 723727830 ATH 689 503095553 ATH 690 463062365 ATH 691 635356752 ATH 692 479815865 ATH 693 241485305 ATH 694 1117006223 ATH 695 379544597 ATH 696 1413201342 ATH 697 737908783 ATH 698 158264787 ATH 699 2952344623 ATH 700 266342372 ATH 701 266932207 ATH 702 518974398 ATH 703 1099292532 ATH 704 224136528 ATH 705 1284198608 ATH 706 879579992 ATH 707 837723670 ATH 708 163229195 ATH 709 255870083 ATH 710 117198610 ATH 711 981031987 ATH 712 473975068 ATH 713 252670687 ATH 714 518521913 ATH 715 281771192 ATH 716 763730312 ATH 717 1194307485 ATH 718 457563965 ATH 719 768783148 ATH 720 1430679030 ATH 721 2981704352 ATH 722 1075227960 ATH 723 645559600 ATH 724 1092654273 ATH 725 1275518800 ATH 726 405648712 ATH 727 1526926895 ATH 728 1257293142 ATH 729 1113658718 ATH 730 330027455 ATH 731 1542800172 ATH 732 1876838155 ATH 733 668620160 ATH 734 1435710433 ATH 735 758035187 ATH 736 460628752 ATH 737 1472270095 ATH 738 990524012 ATH 739 2274128533 ATH 740 666891360 ATH 741 798693837 ATH 742 528848913 ATH 743 1626095195 ATH 744 2027064553 ATH 745 1488413150 ATH 746 3024412342 ATH 747 1120822953 ATH 748 1119254007 ATH 749 1829263013 ATH 750 309474498 ATH 751 2141857912 ATH 752 1188145445 ATH 753 1555699295 ATH 754 1575788473 ATH 755 490061507 ATH 756 1499065927 ATH 757 1430876408 ATH 758 1093950312 ATH 759 658936968 ATH 760 2848292893 ATH 761 965800582 ATH 762 2794651450 ATH 763 1303968270 ATH 764 1816405818 ATH 765 316632998 ATH 766 5053512067 ATH 767 209455865 ATH 768 1026448215 ATH 769 2090858998 ATH 770 1127288990 ATH 771 3219013352 ATH 772 914895105 ATH 773 775537060 ATH 774 3098404998 ATH 775 1771212977 ATH 776 3371708917 ATH 777 982763870 ATH 778 2485321380 ATH 779 1209619483 ATH 780 517354317 ATH 781 2351990732 ATH 782 2284994583 ATH 783 3058180570 ATH 784 2332723393 ATH 785 814993582 ATH 786 2710043882 ATH 787 1602575968 ATH 788 1099506422 ATH 789 3895859993 ATH 790 2275842880 ATH 791 3801465167 ATH 792 1212027450 ATH 793 1109824522 ATH 794 1596204108 ATH 795 116423748 ATH 796 1311811142 ATH 797 3826190170 ATH 798 1838108060 ATH 799 2075033258 ATH 800 2590674053 ATH 801 3991537872 ATH 802 1584876305 ATH 803 688762370 ATH 804 2907115753 ATH 805 1963865683 ATH 806 1218082057 ATH 807 2783167338 ATH 808 1244246607 ATH 809 6688914953 ATH 810 1136057325 ATH 811 4879530092 ATH 812 1078187868 ATH 813 1963011935 ATH 814 2456814678 ATH 815 817898587 ATH 816 2105301987 ATH 817 1476418680 ATH 818 1178478367 ATH 819 2422738013 ATH 820 1150105098 ATH 821 2446124457 ATH 822 2962621393 ATH 823 854904790 ATH 824 3118041113 ATH 825 1596971260 ATH 826 1545818592 ATH 827 1516269855 ATH 828 1080542262 ATH 829 1468003588 ATH 830 2194392940 ATH 831 7926904447 ATH 832 3623219465 ATH 833 2053566580 ATH 834 1701857453 ATH 835 1738411727 ATH 836 521604192 ATH 837 2851193245 ATH 838 707757395 ATH 839 8054272678 ATH 840 1164979197 ATH 841 3999978077 ATH 842 1559932698 ATH 843 4593483547 ATH 844 4196367348 ATH 845 1449938513 ATH 846 3627224892 ATH 847 2271177758 ATH 848 5492863497 ATH 849 6230400578 ATH 850 1203578523 ATH 851 3810733792 ATH 852 2575036223 ATH 853 6060960015 ATH 854 1931713668 ATH 855 1819220120 ATH 856 3172774052 ATH 857 1482890350 ATH 858 4818795527 ATH 859 5689829723 ATH 860 6177395698 ATH 861 2405795462 ATH 862 3026856388 ATH 863 2405159977 ATH 864 11106595143 ATH 865 4289287007 ATH 866 4209447767 ATH 867 3849096298 ATH 868 5069409247 ATH 869 7166434928 ATH 870 2064869648 ATH 871 2476926237 ATH 872 4687880825 ATH 873 4000930010 ATH 874 4776478178 ATH 875 995769922 ATH 876 1233671862 ATH 877 836299100 ATH 878 1323609910 ATH 879 9304370708 ATH 880 2311285048 ATH 881 4678670617 ATH 882 411106845 ATH 883 3147293557 ATH 884 809445493 ATH 885 2306786122 ATH 886 3287184092 ATH 887 1031407750 ATH 888 5187146730 ATH 889 8226414758 ATH 890 3048037043 ATH 891 4781139942 ATH 892 4455278398 ATH 893 5321666817 ATH 894 4568127788 ATH 895 6559094538 ATH 896 3352338792 ATH 897 4322805470 ATH 898 2179079075 ATH 899 2248681003 ATH 900 2238954123 ATH 901 4346895982 ATH 902 7060275863 ATH 903 1223175910 ATH 904 11060909463 ATH 905 1574161108 ATH 906 4349096642 ATH 907 2526316303 ATH 908 5763562942 ATH 909 9224381248 ATH 910 3187343453 ATH 911 4162545082 ATH 912 3920873523 ATH 913 6284266240 ATH 914 7887840663 ATH 915 3964391842 ATH 916 4023472667 ATH 917 4967220493 ATH 918 2785190895 ATH 919 4516769603 ATH 920 1654347340 ATH 921 6886816167 ATH 922 1522788600 ATH 923 1731506367 ATH 924 4163553853 ATH 925 1507820423 ATH 926 6972833117 ATH 927 2528311860 ATH 928 6198848495 ATH 929 5310531548 ATH 930 2689512325 ATH 931 2719152782 ATH 932 6172499860 ATH 933 4207178020 ATH 934 3005762743 ATH 935 4422668477 ATH 936 18462023822 ATH 937 2615806835 ATH 938 4397130915 ATH 939 8493754803 ATH 940 1299446533 ATH 941 8527231937 ATH 942 4945354223 ATH 943 3912129900 ATH 944 13643349213 ATH 945 5531673495 ATH 946 11543632172 ATH 947 4015179735 ATH 948 12862817032 ATH 949 9407061128 ATH 950 5657024718 ATH 951 3749254647 ATH 952 7884111378 ATH 953 3780605152 ATH 954 4441086328 ATH 955 9549957132 ATH 956 9626553492 ATH 957 3765668163 ATH 958 5365459852 ATH 959 14906845753 ATH 960 4077390530 ATH 961 856359122 ATH 962 8640331193 ATH 963 1863989655 ATH 964 10792231053 ATH 965 3157455605 ATH 966 6129872887 ATH 967 9973337810 ATH 968 5706917330 ATH 969 15473299583 ATH 970 3670338742 ATH 971 7514667242 ATH 972 14374380998 ATH 973 5016435072 ATH 974 17508006308 ATH 975 1065472893 ATH 976 4204219947 ATH 977 16162465793 ATH 978 8987211702 ATH 979 9417392003 ATH 980 6262281762 ATH 981 13519426337 ATH 982 10207490848 ATH 983 11779435180 ATH 984 16686552823 ATH 985 13121206348 ATH 986 5917519772 ATH 987 7103990803 ATH 988 3770789082 ATH 989 10920336278 ATH 990 6159537563 ATH 991 3553869007 ATH 992 7971882450 ATH 993 16539204720 ATH 994 3923891423 ATH 995 11323476390 ATH 996 2829945767 ATH 997 8108352970 ATH 998 15359688132 ATH 999 18263276708 ATH 1000 4718578212 ATH 1001 2811629627 ATH 1002 11024680285 ATH 1003 6835356575 ATH 1004 19374221148 ATH 1005 714897587 ATH 1006 14257463852 ATH 1007 4267983675 ATH 1008 10764699650 ATH 1009 18724975378 ATH 1010 4959775740 ATH 1011 6904565602 ATH 1012 6009418280 ATH 1013 6582996530 ATH 1014 11991672908 ATH 1015 7504060620 ATH 1016 12499155547 ATH 1017 8955975688 ATH 1018 5986929792 ATH 1019 7242983443 ATH 1020 13688528333 ATH 1021 12937575437 ATH 1022 6003407428 ATH 1023 8561645130 ATH 1024 30370627668 ATH 1025 16507782197 ATH 1026 12133392337 ATH 1027 8527092578 ATH 1028 5400391645 ATH 1029 8780665563 ATH 1030 5007391888 ATH 1031 8309499172 ATH 1032 3740360183 ATH 1033 12579042990 ATH 1034 7490905648 ATH 1035 4354724050 ATH 1036 12790338547 ATH 1037 14585762935 ATH 1038 12918899037 ATH 1039 10528753153 ATH 1040 8643398725 ATH 1041 22228983707 ATH 1042 18421312110 ATH 1043 4277863287 ATH 1044 22247337703 ATH 1045 9117393532 ATH 1046 11812293782 ATH 1047 3196956045 ATH 1048 7919321767 ATH 1049 10991916183 ATH 1050 9865733768 ATH 1051 22563333397 ATH 1052 22070444965 ATH 1053 16686868527 ATH 1054 12996465758 ATH 1055 8472371157 ATH 1056 31366197567 ATH 1057 9491799368 ATH 1058 8659623317 ATH 1059 11055610988 ATH 1060 13235724187 ATH 1061 41915068062 ATH 1062 18498428755 ATH 1063 9023952725 ATH 1064 9653598588 ATH 1065 5298861998 ATH 1066 12036778707 ATH 1067 14334530700 ATH 1068 39987891870 ATH 1069 22736738038 ATH 1070 4416179072 ATH 1071 12539957742 ATH 1072 25946320698 ATH 1073 14636179420 ATH 1074 12432480398 ATH 1075 7762655897 ATH 1076 19372935412 ATH 1077 14255597088 ATH 1078 16521687485 ATH 1079 4035849583 ATH 1080 24070972425 ATH 1081 21562226522 ATH 1082 14943718163 ATH 1083 13624623332 ATH 1084 18383401348 ATH 1085 15837017163 ATH 1086 43177754272 ATH 1087 18253515870 ATH 1088 17472321867 ATH 1089 11557132158 ATH 1090 8186246962 ATH 1091 41500930727 ATH 1092 4142929803 ATH 1093 9490473660 ATH 1094 21439776823 ATH 1095 40213458707 ATH 1096 28895725292 ATH 1097 21386758558 ATH 1098 25137783535 ATH 1099 29311613548 ATH 1100 14524563518 ATH 1101 12875454587 ATH 1102 10942894720 ATH 1103 11202556685 ATH 1104 16615629933 ATH 1105 16606921495 ATH 1106 20860243742 ATH 1107 17500043025 ATH 1108 6708903010 ATH 1109 19821577948 ATH 1110 12852163973 ATH 1111 8412207522 ATH 1112 25186770675 ATH 1113 14333623160 ATH 1114 23078677218 ATH 1115 9254604950 ATH 1116 15134152567 ATH 1117 24189828365 ATH 1118 29646936667 ATH 1119 34226827423 ATH 1120 18463125062 ATH 1121 58663327587 ATH 1122 10133636193 ATH 1123 26227925140 ATH 1124 42383800163 ATH 1125 38347022838 ATH 1126 20497482947 ATH 1127 8185647088 ATH 1128 29451224835 ATH 1129 29579425773 ATH 1130 16298537952 ATH 1131 37485937562 ATH 1132 7578097340 ATH 1133 25913710302 ATH 1134 14524565688 ATH 1135 20792431795 ATH 1136 28809229977 ATH 1137 13582827433 ATH 1138 37975916165 ATH 1139 61756317343 ATH 1140 15892671560 ATH 1141 10439154257 ATH 1142 25262591533 ATH 1143 28593081655 ATH 1144 48826150303 ATH 1145 41705622962 ATH 1146 25794434892 ATH 1147 16293399008 ATH 1148 8582270267 ATH 1149 8525721438 ATH 1150 16251349042 ATH 1151 45316370542 ATH 1152 21034892753 ATH 1153 15728686990 ATH 1154 17504175188 ATH 1155 24735441112 ATH 1156 33174606362 ATH 1157 27616548440 ATH 1158 42035688247 ATH 1159 23092251588 ATH 1160 14998583343 ATH 1161 56801711312 ATH 1162 29812173248 ATH 1163 17756220570 ATH 1164 16797436063 ATH 1165 14435182932 ATH 1166 15804331282 ATH 1167 33766997653 ATH 1168 29664641207 ATH 1169 51537427428 ATH 1170 25320667690 ATH 1171 21420242172 ATH 1172 39668112358 ATH 1173 13791132407 ATH 1174 18761657808 ATH 1175 7073619248 ATH 1176 30537616247 ATH 1177 23153721783 ATH 1178 15554271252 ATH 1179 57841170578 ATH 1180 13255405793 ATH 1181 31234475137 ATH 1182 30924553110 ATH 1183 26168680170 ATH 1184 49319201213 ATH 1185 23812067153 ATH 1186 41936084087 ATH 1187 8939732550 ATH 1188 14330487105 ATH 1189 44674906188 ATH 1190 8031358767 ATH 1191 10603108182 ATH 1192 18835412365 ATH 1193 34746153190 ATH 1194 16560031848 ATH 1195 9391637273 ATH 1196 14528709892 ATH 1197 18242511845 ATH 1198 25046740252 ATH 1199 33650418018 ATH 1200 18359485235 ATH 1201 33051842117 ATH 1202 66002847468 ATH 1203 26782423792 ATH 1204 40847394758 ATH 1205 15928146832 ATH 1206 64999749057 ATH 1207 9988457248 ATH 1208 19986121662 ATH 1209 53500919883 ATH 1210 29408935490 ATH 1211 32056558362 ATH 1212 46819768958 ATH 1213 23359512832 ATH 1214 20331890558 ATH 1215 36293533640 ATH 1216 68006592497 ATH 1217 48101859580 ATH 1218 35070286585 ATH 1219 10774224213 ATH 1220 36726742647 ATH 1221 25678337692 ATH 1222 8695593693 ATH 1223 43949266767 ATH 1224 90705803338 ATH 1225 25905710483 ATH 1226 35530520182 ATH 1227 50758082210 ATH 1228 43848563047 ATH 1229 44351452008 ATH 1230 26404449530 ATH 1231 101208274662 ATH 1232 22556325743 ATH 1233 37269319510 ATH 1234 45484451658 ATH 1235 41601982865 ATH 1236 20875795512 ATH 1237 56829323030 ATH 1238 32867985517 ATH 1239 33904468903 ATH 1240 37951687547 ATH 1241 23524711222 ATH 1242 51497620853 ATH 1243 64872205377 ATH 1244 65789117053 ATH 1245 57057845338 ATH 1246 40884738972 ATH 1247 36050767643 ATH 1248 53024192545 ATH 1249 48725636383 ATH 1250 28543693757 ATH 1251 64133691577 ATH 1252 45976631095 ATH 1253 56015688972 ATH 1254 100761544543 ATH 1255 22544518132 ATH 1256 38237309287 ATH 1257 37685943368 ATH 1258 20020326737 ATH 1259 89817312058 ATH 1260 40437430637 ATH 1261 81952221312 ATH 1262 34386364680 ATH 1263 64312175652 ATH 1264 41031871478 ATH 1265 7595970438 ATH 1266 66001896202 ATH 1267 102711625448 ATH 1268 52055075942 ATH 1269 60464331573 ATH 1270 26072298478 ATH 1271 94947179337 ATH 1272 37482239365 ATH 1273 52338755872 ATH 1274 31605073873 ATH 1275 37883577230 ATH 1276 19485934097 ATH 1277 10846539718 ATH 1278 53318021160 ATH 1279 80634404163 ATH 1280 40551655827 ATH 1281 31260613627 ATH 1282 51115333138 ATH 1283 69732506812 ATH 1284 70023017393 ATH 1285 12347431502 ATH 1286 41906763817 ATH 1287 29873248415 ATH 1288 29314359620 ATH 1289 44402436488 ATH 1290 43944263470 ATH 1291 60328695492 ATH 1292 35124127965 ATH 1293 44978931772 ATH 1294 78981727158 ATH 1295 66748779720 ATH 1296 136174101612 ATH 1297 83379921555 ATH 1298 9634521157 ATH 1299 29706714558 ATH 1300 59173429653 ATH 1301 64935700882 ATH 1302 77686997383 ATH 1303 68044441195 ATH 1304 40831407493 ATH 1305 24030385738 ATH 1306 37042953262 ATH 1307 92308689725 ATH 1308 91890048212 ATH 1309 69089723273 ATH 1310 71131302125 ATH 1311 65562906117 ATH 1312 50485273458 ATH 1313 48624178687 ATH 1314 83852500748 ATH 1315 48882377632 ATH 1316 75146429732 ATH 1317 36692181453 ATH 1318 53992589912 ATH 1319 186438133443 ATH 1320 51173468143 ATH 1321 30530362357 ATH 1322 94707449170 ATH 1323 42450011142 ATH 1324 70051577718 ATH 1325 40320006480 ATH 1326 78720103417 ATH 1327 31520502065 ATH 1328 34445495270 ATH 1329 143446677043 ATH 1330 7287610437 ATH 1331 86046387072 ATH 1332 51772611128 ATH 1333 104162957980 ATH 1334 44438479298 ATH 1335 46412332407 ATH 1336 92479857902 ATH 1337 51780274385 ATH 1338 97017192822 ATH 1339 79715880988 ATH 1340 10849288625 ATH 1341 82083852107 ATH 1342 132223116333 ATH 1343 25083224815 ATH 1344 62994611978 ATH 1345 78773730823 ATH 1346 103895222522 ATH 1347 66824446040 ATH 1348 93470563142 ATH 1349 46032970723 ATH 1350 110940120422 ATH 1351 147555423337 ATH 1352 44028349955 ATH 1353 72388630452 ATH 1354 176010608498 ATH 1355 35415187398 ATH 1356 73721641492 ATH 1357 39997802863 ATH 1358 68875590515 ATH 1359 238021889388 Thomas11 1360 120701590522 ATH 1361 103656076897 ATH 1362 129780127055 ATH 1363 45464706810 ATH 1364 236116004983 Thomas11 1365 27432631065 ATH 1366 221323766702 Thomas11 1367 66664704428 ATH 1368 79675959260 ATH 1369 105795508798 ATH 1370 22751684835 ATH 1371 150422884902 ATH 1372 73987959848 ATH 1373 91101657665 ATH 1374 74619205678 ATH 1375 106433204497 ATH 1376 109109662112 ATH 1377 140926519020 ATH 1378 158222902962 ATH 1379 59513006413 ATH 1380 83535481318 ATH 1381 81120569787 ATH 1382 208297454633 Thomas11 1383 82037154155 ATH 1384 91105669713 ATH 1385 35954269187 ATH 1386 36654125322 ATH 1387 82436707565 ATH 1388 52106714982 ATH 1389 335699670478 Thomas11 1390 134783026287 ATH 1391 91527303572 ATH 1392 160241217295 ATH 1393 78441568602 ATH 1394 107218832948 ATH 1395 93204583073 ATH 1396 370369427962 Thomas11 1397 71529209675 ATH 1398 89717150497 ATH 1399 167763335213 ATH 1400 78769799252 ATH 1401 113406055667 ATH 1402 83591984703 ATH 1403 209318000600 Thomas11 1404 115946907303 ATH 1405 60066856568 ATH 1406 157757582267 ATH 1407 207000817860 Thomas11 1408 75688827280 ATH 1409 131711929323 ATH 1410 199574686315 ATH 1411 48278160327 ATH 1412 157757709578 ATH 1413 32135929095 ATH 1414 179075794238 ATH 1415 49037845735 ATH 1416 64167955752 ATH 1417 117577979190 ATH 1418 108513597027 ATH 1419 77078300443 ATH 1420 74951308542 ATH 1421 42119304362 ATH 1422 101735004478 ATH 1423 142152878497 ATH 1424 258224787443 Thomas11 1425 88942037140 ATH 1426 114261540757 ATH 1427 228073106628 Thomas11 1428 100389566412 ATH 1429 175835907578 ATH 1430 48978765967 ATH 1431 105371512887 ATH 1432 89851341625 ATH 1433 211777215930 Thomas11 1434 197709087693 ATH 1435 110562730142 ATH 1436 34440671017 ATH 1437 141185526520 ATH 1438 167850568830 ATH 1439 94595234198 ATH 1440 34516209527 ATH 1441 195969981917 ATH 1442 136888972125 ATH 1443 134581666552 ATH 1444 159728123338 ATH 1445 38840382823 ATH 1446 227253338462 Thomas11 1447 57301290370 ATH 1448 77920988750 ATH 1449 102332614223 ATH 1450 108516370937 ATH 1451 64095115322 ATH 1452 151527991675 ATH 1453 145272707550 ATH 1454 174799142838 ATH 1455 81631078743 ATH 1456 195778814802 ATH 1457 301410421995 Thomas11 1458 264657155665 Thomas11 1459 206268027728 Thomas11 1460 64584093742 ATH 1461 472019855132 Thomas11 1462 88475830910 ATH 1463 69741598787 ATH 1464 224994765053 Thomas11 1465 135767046975 ATH 1466 275157656942 Thomas11 1467 85661945075 ATH 1468 63139736062 ATH 1469 228677692513 Thomas11 1470 106208976653 ATH 1471 156171984272 ATH 1472 138299223690 ATH 1473 184783689402 ATH 1474 365110475063 Thomas11 1475 67410836280 ATH 1476 267918092432 Thomas11 1477 185821439738 ATH 1478 96139203857 ATH 1479 214041248743 Thomas11 1480 240784621312 Thomas11 1481 228476499377 Thomas11 1482 176427443750 ATH 1483 48773094382 ATH 1484 136319467498 ATH 1485 169809420105 ATH 1486 150516739082 ATH 1487 405178602348 Thomas11 1488 209618644275 Thomas11 1489 130741136258 ATH 1490 88340661855 ATH 1491 227858144272 Thomas11 1492 121639858400 ATH 1493 66924164457 ATH 1494 406142933448 Thomas11 1495 69782047618 ATH 1496 174973906777 ATH 1497 291869230735 Thomas11 1498 308394175852 Thomas11 1499 22339570278 ATH 1500 172823544343 ATH 1501 326074608547 Thomas11 1502 128837925765 ATH 1503 181674927455 ATH 1504 289506845778 Thomas11 1505 160823433270 ATH 1506 227491883602 Thomas11 1507 176020578323 ATH 1508 279911847660 Thomas11 1509 434412984948 Thomas11 1510 163775464003 ATH 1511 393469552312 Thomas11 1512 218349176503 Thomas11 1513 342721571537 Thomas11 1514 440909475828 Thomas11 1515 155390806498 ATH 1516 85283577452 ATH 1517 196413282468 ATH 1518 184159612907 ATH 1519 235557862248 Thomas11 1520 159460255028 ATH 1521 359489269902 Thomas11 1522 219322573465 Thomas11 1523 147488057610 ATH 1524 263159931988 Thomas11 1525 98616660978 ATH 1526 56105289977 ATH 1527 194013931730 ATH 1528 263122426457 Thomas11 1529 137914593968 ATH 1530 164942161335 ATH 1531 82643395422 ATH 1532 238243169945 Thomas11 1533 247333123902 Thomas11 1534 450299367998 Thomas11 1535 328710671530 Thomas11 1536 151913191462 ATH 1537 343278293043 Thomas11 1538 119496454527 ATH 1539 225373027793 Thomas11 1540 139666887840 ATH 1541 251898401212 Thomas11 1542 181392272663 ATH 1543 180056667807 ATH 1544 146578135928 ATH 1545 70464152903 ATH 1546 168996745347 ATH 1547 160429275275 ATH 1548 142976782372 ATH 1549 170014476063 ATH 1550 174553795390 ATH 1551 222454633082 Thomas11 1552 33051947625 ATH 1553 37182176622 ATH 1554 344855543718 Thomas11 1555 119208146283 ATH 1556 107282165062 ATH 1557 143282458305 ATH 1558 164872223950 ATH 1559 385122746008 Thomas11 1560 62578713270 ATH 1561 176158811742 ATH 1562 118027566675 ATH 1563 364921287610 Thomas11 1564 299852086093 Thomas11 1565 136243056022 ATH 1566 399858131992 Thomas11 1567 223700692605 Thomas11 1568 359606250350 Thomas11 1569 558397733113 Thomas11 1570 206516426483 Thomas11 1571 281055726357 Thomas11 1572 215157908388 Thomas11 1573 248533440965 Thomas11 1574 605483702178 Thomas11 1575 103750795712 ATH 1576 278322616602 Thomas11 1577 185624758875 ATH 1578 354907107055 Thomas11 1579 275064432933 Thomas11 1580 184298726117 ATH 1581 513934851092 Thomas11 1582 383060493443 Thomas11 1583 129919858890 ATH 1584 550087135293 Thomas11 1585 96643867775 ATH 1586 244777442157 Thomas11 1587 144666194755 ATH 1588 317882759267 Thomas11 1589 504467037198 Thomas11 1590 116320889387 ATH 1591 552495066182 Thomas11 1592 385287103058 Thomas11 1593 307663309660 Thomas11 1594 268309573438 Thomas11 1595 177702480225 ATH 1596 255548544727 Thomas11 1597 785707760883 Thomas11 1598 276185251937 Thomas11 1599 310000481863 Thomas11 1600 243015237435 Thomas11 1601 476094473867 Thomas11 1602 401584755318 Thomas11 1603 121584681445 ATH 1604 333819870513 Thomas11 1605 185545828858 ATH 1606 809203672447 Thomas11 1607 220818051338 Thomas11 1608 562941500147 Thomas11 1609 566988071438 Thomas11 1610 109354338662 ATH 1611 538043378982 Thomas11 1612 383806176040 Thomas11 1613 128518326722 ATH 1614 425743230153 Thomas11 1615 210586309103 Thomas11 1616 601754613962 Thomas11 1617 211557516208 Thomas11 1618 151521188780 ATH 1619 261923049103 Thomas11 1620 111423209912 ATH 1621 466752047347 Thomas11 1622 395629846073 Thomas11 1623 284209749890 Thomas11 1624 201089339318 Thomas11 1625 297772201955 Thomas11 1626 354443118657 Thomas11 1627 538605605153 Thomas11 1628 563886417640 Thomas11 1629 450374566348 Thomas11 1630 280475819957 Thomas11 1631 117959421867 ATH 1632 256713987023 Thomas11 1633 103293294022 ATH 1634 432495163513 Thomas11 1635 101323871015 ATH 1636 1035211477332 robert44444uk 1637 314387243880 Thomas11 1638 223187612730 Thomas11 1639 430370370398 Thomas11 1640 251399472527 Thomas11 1641 272511992827 Thomas11 1642 212024898078 Thomas11 1643 158850706422 ATH 1644 1201386008933 robert44444uk 1645 464373757405 Thomas11 1646 197557993677 ATH 1647 384183995148 Thomas11 1648 555439323975 Thomas11 1649 158176828393 ATH 1650 409316753062 Thomas11 1651 312158180092 Thomas11 1652 470531332488 Thomas11 1653 841664786197 Thomas11 1654 701771647838 Thomas11 1655 405384059735 Thomas11 1656 514927351307 Thomas11 1657 229220533173 Thomas11 1658 166226961612 ATH 1659 165136905488 ATH 1660 133864375453 ATH 1661 633288781027 Thomas11 1662 256117920503 Thomas11 1663 492030454557 Thomas11 1664 131415761768 ATH 1665 291876048707 Thomas11 1666 802227020182 Thomas11 1667 375860209433 Thomas11 1668 285028014162 Thomas11 1669 859713724753 Thomas11 1670 295839732305 Thomas11 1671 579035340417 Thomas11 1672 161263436148 ATH 1673 498618428432 Thomas11 1674 636283516158 Thomas11 1675 616638723823 Thomas11 1676 859939543782 Thomas11 1677 508171256813 Thomas11 1678 487863089385 Thomas11 1679 600200255728 Thomas11 1680 448760176352 Thomas11 1681 569028734977 Thomas11 1682 280877509220 Thomas11 1683 1019626449685 robert44444uk 1684 435854938013 Thomas11 1685 256321846760 Thomas11 1686 1025620695957 robert44444uk 1687 156290145345 ATH 1688 611197905670 Thomas11 1689 984424116398 Thomas11 1690 652938228583 Thomas11 1691 463542106657 Thomas11 1692 254281560703 Thomas11 1693 431955803822 Thomas11 1694 334135265893 Thomas11 1695 282763122140 Thomas11 1696 450016651352 Thomas11 1697 822643098295 Thomas11 1698 565141146050 Thomas11 1699 372837607753 Thomas11 1700 58917239540 ATH 1701 433407295157 Thomas11 1702 298348323303 Thomas11 1703 466812660410 Thomas11 1704 1045077852373 robert44444uk 1705 517453687215 Thomas11 1706 772867305887 Thomas11 1707 524920422073 Thomas11 1708 459952950865 Thomas11 1709 515336777288 Thomas11 1710 89470349442 ATH 1711 1437737041932 robert44444uk 1712 567801655963 Thomas11 1713 216733386980 Thomas11 1714 1039648289663 robert44444uk 1715 555007406300 Thomas11 1716 485816451332 Thomas11 1717 504463536573 Thomas11 1718 661561148110 Thomas11 1719 325264034063 Thomas11 1720 453489992522 Thomas11 1721 1253001163102 robert44444uk 1722 610655512490 Thomas11 1723 80799633875 ATH 1724 634233966553 Thomas11 1725 762318092370 Thomas11 1726 261705340277 Thomas11 1727 225881516975 Thomas11 1728 538335755667 Thomas11 1729 806506374413 Thomas11 1730 217895151387 Thomas11 1731 707703825092 Thomas11 1732 735596463515 Thomas11 1733 768450016780 Thomas11 1734 745631868578 Thomas11 1735 356177753412 Thomas11 1736 741222736422 Thomas11 1737 761250576468 Thomas11 1738 671721527412 Thomas11 1739 1214363016178 robert44444uk 1740 384364766532 Thomas11 1741 563317414062 Thomas11 1742 724809604908 Thomas11 1743 370979739580 Thomas11 1744 359521940948 Thomas11 1745 300186232845 Thomas11 1746 447197130142 Thomas11 1747 907203956603 Thomas11 1748 528077281142 Thomas11 1749 801659775458 Thomas11 1750 280488680647 Thomas11 1751 739849772267 Thomas11 1752 496386470473 Thomas11 1753 714960674750 Thomas11 1754 338841041033 Thomas11 1755 532001966893 Thomas11 1756 671605907382 Thomas11 1757 294509651840 Thomas11 1758 1278737589385 robert44444uk 1759 298338286438 Thomas11 1760 1175000358333 robert44444uk 1761 584390565997 Thomas11 1762 318182662973 Thomas11 1763 600635385640 Thomas11 1764 240121693893 Thomas11 1765 1204735995605 robert44444uk 1766 473256996777 Thomas11 1767 828485975438 Thomas11 1768 1176057612252 robert44444uk 1769 782711361523 Thomas11 1770 855953593323 Thomas11 1771 988638208437 Thomas11 1772 655550748640 Thomas11 1773 411932055292 Thomas11 1774 447362234533 Thomas11 1775 449770326922 Thomas11 1776 805225566947 Thomas11 1777 550358556340 Thomas11 1778 106405396032 ATH Code:
1780 982232544190 Thomas11 1781 841171099652 Thomas11 1782 1224262909268 robert44444uk 1783 1422392477865 robert44444uk 1784 1195747448213 robert44444uk 1785 130744752537 ATH 1786 825384984377 Thomas11 1787 776268942683 Thomas11 1788 854615602792 Thomas11 1789 646099785688 Thomas11 1790 557950608758 Thomas11 1791 369489065347 Thomas11 1792 689680764418 Thomas11 1793 1037083894142 robert44444uk 1794 621462178578 Thomas11 1795 750466894258 Thomas11 1797 582262097498 Thomas11 1798 608219715197 Thomas11 1799 244370452833 Thomas11 1800 831467803302 Thomas11 1801 1052870164587 robert44444uk 1802 800163087448 Thomas11 1803 1306998722697 robert44444uk 1804 1382597845958 robert44444uk 1805 1166113583162 robert44444uk 1806 363596492507 Thomas11 1807 589681107438 Thomas11 1808 374311870175 Thomas11 1809 1519940585608 robert44444uk 1810 133135498198 ATH 1811 754512505717 Thomas11 1812 1225517231188 robert44444uk 1813 1177115829552 robert44444uk 1814 1622632461223 robert44444uk 1815 169866686215 ATH 1816 536707956407 Thomas11 1817 956610710023 Thomas11 1818 707849433580 Thomas11 1819 478026230448 Thomas11 1820 524708956392 Thomas11 1821 1545928373782 robert44444uk 1822 363792713305 Thomas11 1823 393901596172 Thomas11 1825 718703397508 Thomas11 1826 1197393987332 robert44444uk 1827 514690190788 Thomas11 1828 544205194130 Thomas11 1829 1682087625368 robert44444uk 1830 283716126022 Thomas11 1831 1024442893122 robert44444uk 1832 746075980130 Thomas11 1833 1171018474300 robert44444uk 1834 1461304039818 robert44444uk 1835 1236784093577 robert44444uk 1836 663607308612 Thomas11 1837 361289615670 Thomas11 1838 284106487357 Thomas11 1839 1320327308713 robert44444uk 1840 389453919375 Thomas11 1841 738549390442 Thomas11 1842 1084227409855 robert44444uk 1843 737313907580 Thomas11 1845 1537365969212 robert44444uk 1846 823245280032 Thomas11 1847 675857800098 Thomas11 1848 723741177537 Thomas11 1850 804839675663 Thomas11 1851 363074768532 Thomas11 1853 932204536545 Thomas11 1854 1189288485208 robert44444uk 1855 1174605355802 robert44444uk 1856 1297574083922 robert44444uk 1857 729575524785 Thomas11 1858 1123294853522 robert44444uk 1860 843314053692 Thomas11 1862 663487911713 Thomas11 1863 336185917595 Thomas11 1864 1417574651223 robert44444uk 1865 781793275960 Thomas11 1866 892852657037 Thomas11 1867 1444042188138 robert44444uk 1870 513194527407 Thomas11 1871 971781746092 Thomas11 1872 447811616018 Thomas11 1873 1348365096302 robert44444uk 1874 750393104603 Thomas11 1875 598433097470 Thomas11 1876 1064530504212 robert44444uk 1877 1040113573768 robert44444uk 1878 1694010994357 robert44444uk 1880 904212211453 Thomas11 1881 781557375732 Thomas11 1882 1375789467133 robert44444uk 1883 1086233157432 robert44444uk 1885 676152407723 Thomas11 1887 426285083663 Thomas11 1888 1709285542095 robert44444uk 1890 151287342070 ATH 1891 1247181224132 robert44444uk 1892 201865544225 Thomas11 1893 290614184492 Thomas11 1894 1666811164798 robert44444uk 1895 854745621275 Thomas11 1897 359738661993 Thomas11 1898 132437316545 ATH 1900 619983477157 Thomas11 1901 635700745862 Thomas11 1902 1068189680728 robert44444uk 1903 675525244735 Thomas11 1905 932239203395 Thomas11 1906 1279486288362 robert44444uk 1907 1202177228578 robert44444uk 1908 1222826404275 robert44444uk 1910 1551507663815 robert44444uk 1911 1670504219247 robert44444uk 1912 804438922933 Thomas11 1914 1488017568723 robert44444uk 1915 470420475572 Thomas11 1917 1165423934903 robert44444uk 1918 804794472115 Thomas11 1919 1572478640448 robert44444uk 1923 1395252802692 robert44444uk 1924 1696444081623 robert44444uk 1925 523274691888 Thomas11 1926 696620005307 Thomas11 1928 1181669865490 robert44444uk 1932 960136903043 Thomas11 1933 1521234330052 robert44444uk 1934 1368396113168 robert44444uk 1935 664808242868 Thomas11 1936 279967183457 Thomas11 1937 642270715125 Thomas11 1940 1435690154763 robert44444uk 1941 1675555446682 robert44444uk 1943 1042310309512 robert44444uk 1945 1194795033583 robert44444uk 1946 1267188286017 robert44444uk 1947 1501956317263 robert44444uk 1950 982578277387 Thomas11 1953 954508482785 Thomas11 1955 511426336883 Thomas11 1958 757895739535 Thomas11 1960 1603135467927 robert44444uk 1964 1717072682918 robert44444uk 1968 652547157105 Thomas11 1969 1116171078598 robert44444uk 1971 824751367527 Thomas11 1972 1484101843865 robert44444uk 1976 1629196186112 robert44444uk 1979 614991456963 Thomas11 1984 564720846228 Thomas11 1985 1432632140313 robert44444uk 1986 944675774037 Thomas11 1987 645901356965 Thomas11 1990 1178585706107 robert44444uk 1993 1333290080990 robert44444uk 1994 721147884418 Thomas11 1995 1081507694722 robert44444uk 1997 207741061965 Thomas11 2002 1418099818398 robert44444uk 2006 541952390642 Thomas11 2007 1294793177503 robert44444uk 2012 1355880364715 robert44444uk 2013 1605983743805 robert44444uk 2015 1366762534618 robert44444uk 2016 389348710292 Thomas11 2018 1320531199235 robert44444uk 2020 1110837159180 robert44444uk 2023 224142765215 Thomas11 2027 1513315229030 robert44444uk 2028 1693568705267 robert44444uk 2029 548899132323 Thomas11 2030 1159591145647 robert44444uk 2031 1505148947332 robert44444uk 2032 801995327063 Thomas11 2040 1457630950535 robert44444uk 2042 1102539778813 robert44444uk 2045 1654904607582 robert44444uk 2048 249479281077 Thomas11 2057 1327506760473 robert44444uk 2060 1506078160848 robert44444uk 2068 1462559617500 robert44444uk 2070 1042838539733 robert44444uk 2072 461157712565 Thomas11 2073 902743525100 Thomas11 2074 646834943323 Thomas11 2075 1226421246838 robert44444uk 2080 665814402872 Thomas11 2081 1557362375067 robert44444uk 2086 518189243667 Thomas11 2090 524000762887 Thomas11 2093 362104284385 Thomas11 2096 654588515312 Thomas11 2103 1654754653500 robert44444uk 2105 359442044602 Thomas11 2109 1543363000013 robert44444uk 2110 1612044398132 robert44444uk 2113 1096035536635 robert44444uk 2125 1542932450388 robert44444uk 2134 1576063926063 robert44444uk 2163 509866874615 Thomas11 2175 405935625685 Thomas11 2183 823397649847 Thomas11 2198 1225499177052 robert44444uk 2219 1346519039873 robert44444uk 2228 986150450957 Thomas11 2255 1108236319297 robert44444uk 2267 1360918509703 robert44444uk 2297 1379963970150 robert44444uk 2299 1646969192138 robert44444uk 2305 1094577877207 robert44444uk 2357 1606989456770 robert44444uk 2377 748572833888 Thomas11 |
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2019-04-29, 13:00
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#19 |
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Jun 2003
Suva, Fiji
23·3·5·17 Posts |
Here's an interesting graph which shows the frequency of all gaps between consecutive twin prime pairs. The population of gaps represents all k between 1 and approx. 4.43e7.
Not all gap lengths are equal in frequency. Those that do relatively poorly are lengths which are highly composite, especially with prime factors 2 and 3. Those that do well are multiples of 5,7,11,13... In the graph -
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2019-04-29, 14:07
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#20 |
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Jun 2003
Suva, Fiji
23×3×5×17 Posts |
Regarding the graph above, I not at all sure about gaps 0mod11, 0mod13 etc.. Here are some stats on the first 1.666e9k
There were 27,412,678 twin prime gaps, of which 8,632,028 were 0 mod5 3,221,541 were 1 mod5 6,415,438 were 2 mod5 6,086,566 were 3 mod5 3,057,104 were 4 mod5 So the 0mod5 case is made. 4,955,717 were 0 mod7 3,481,004 were 1 mod7 4,418,659 were 2 mod7 3,464,620 were 3 mod7 3,288,570 were 4 mod7 4,510,772 were 5 mod7 3,293,335 were 6 mod7 The 0mod 7 was not at all dominant in the early stages but appears to be in ascendancy the higher the k. 2,526,237 were 0 mod11 2,459,124 were 1 mod11 2,766,048 were 2 mod11 2,398,069 were 3 mod11 2,707,618 were 4 mod11 2,537,710 were 5 mod11 2,303,639 were 6 mod11 2,833,137 were 7 mod11 2,370,441 were 8 mod11 2,171,210 were 9 mod11 2,339,444 were 10 mod11 0mod13 does not show positive tendencies either. For the small range from 1e9 covering an additional 1.667e5 k continues to show strong bias towards 0mod5, and a lesser bias towards 0mod7 but none towards 0mod11. There is some proper modular maths going on here to show such strong bias towards 0mod5, and a strong negative bias towards 1mod5 and 4mod5 Last fiddled with by robert44444uk on 2019-04-29 at 14:12 |
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2019-04-29, 19:00
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#21 | |
Dec 2008
you know...around...
11010100002 Posts |
Quote:
Code:
number of open residues mod... k%5: pattern : 5 7 11 13 0: 0 2 30 32 : 3 4 7 9 = 756 in 30030 1: 0 2 6 8 : 1 3 7 9 = 189 in 30030 2: 0 2 12 14 : 2 4 7 9 = 504 in 30030 3: 0 2 18 20 : 2 3 7 9 = 378 in 30030 4: 0 2 24 26 : 1 3 8 10 = 240 in 30030 Continuing this line of argumentation should yield good approximations. Maybe I can work out some details tomorrow. |
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2019-04-30, 07:43
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#22 | |
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Jun 2003
Suva, Fiji
23×3×5×17 Posts |
Quote:
Last fiddled with by robert44444uk on 2019-04-30 at 07:56 |
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