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The trophy case table below shows first known occurances of super-dense k-tuples.
The first column shows the number of additional primes that can be packed in the
interval, as a contradiction to a Hardy-Littlewood conjecture.

Additions to the table can be posted by sending the residue sets or a listing of prime positions
for the width to be added.  Please send any additions to tom(at)opertech.com

Last update : 12-Sep-09

Trophy Case

k-p(w) width k year by +1 3159 447 see note +2 3241 459 2004 TE +3 3243 460 +4 4589 624 +5 4875 657 +6 4899 660 +7 5365 715   +8 5371 716 +9 6541 853 2005 JW +10 6647 866       +11 7359 946 +12 7367 949 +13 7387 951 +14 7401 953 +15 7429 956 +16 7441 958 +17 7445 959 +18 10031 1249 +19 10413 1293 +20 10423 1294 +21 10451 1298 +22 10543 1310 +23 10555 1311 +24 10821 1339 +25 10931 1351 +26 11045 1363 2006 * +27 11575 1419   +28 11577 1420 +29 11671 1429 +30 11773 1439 +31 13581 1637 +32 13609 1640 +33 14137 1696 +34 14227 1706 +35 14229 1707 +36 14239 1708 +37 14301 1714 k-p(w) width k year by +38 14317 1716   +39 14373 1723 +40 14379 1724 +41 16629 1963 +42 16807 1981 +43 16857 1987 +44 16867 1988 +45 17165 2021 +46 17179 2023 +47 17275 2033 +48 18667 2179 +49 18709 2184 +50 18855 2197 +51 18889 2200 +52 18897 2201 +53 18967 2209 +54 18991 2212 +55 18999 2213 +56 19155 2228 +57 19201 2233 +58 19349 2249 +59 19357 2250 +60 19369 2651 +61 22917 2618 +62 22927 2620 +63 22991 2626 +64 23403 2671 +65 23409 2672 +66 23413 2673 +67 23465 2678 +68 23471 2679 +69 23507 2682 +70 23521 2684 +71 23529 2685 +72 24741 2809 +73 24837 2818 +74 24915 2826 k-p(w) width k year by +75 25095 2844 +76 25291 2864 +77 25443 2881 +78 25513 2888 +79 25563 2893 +80 26549 2993 +81 26587 2997 +82 26623 3000 +83 26667 3005 +84 27387 3077 +85 27391 3078 +86 27519 3091 +87 27523 3092 +88 27609 3100 +89 27687 3107 +90 27727 3112 +91 28255 3168 +92 28259 3169 +93 28273 3170 +94 28377 3181 +95 28383 3182 +96 28511 3196 +97 29829 3327 +98 29905 3336 +99 29915 3337 +100 30001 3345 +101 30043 3349 +102 30069 3352 +103 30457 3391 +104 30487 3394 +105 30627 3407 +106 30827 3428 +107 31003 3447 +108 31829 3528 +109 31837 3529 +110 31931 3537 +111 31945 3538 k-p(w) width k year by +112 31951 3539   +113 34111 3757 +114 34115 3758 +115 35043 3849 +116 35255 3871 +117 35719 3912 +118 35725 3913 +119 35793 3920 +120 36425 3981 +121 36445 3983 +122 37825 4122 +123 37923 4132 +124 37939 4133 +125 38111 4148 +126 38147 4151 +127 38527 4186 +128 38535 4187 +129 38551 4189 +130 38591 4194 +131 39579 4294 +132 39599 4296 +133 39617 4298 +134 39815 4317 +135 40273 4363 +136 40299 4367 +137 40309 4368 +138 40319 4369 +139 40327 4370 +140 40333 4371 +141 40385 4376 +142 40403 4378 +143 40415 4379 +144 40421 4380 +145 41105 4445 +146 41439 4480 +147 41465 4483 +148 41503 4487

The 447-tuple was independently found by Ralph Gasser/Prof. Joerg Waldvogel, Mischa Kenn, and Thomas J Engelsma TE -- Thomas J Engelsma JW-- Prof. Joerg Waldvogel * -- created by Thomas J Engelsma from tuples submitted by Prof. Joerg Waldvogel blank -- progress of searches by Thomas J Engelsma using sub-patterns from all existing tuples The links to the raw data are to ASCII text files. The data is in half-difference format.

Graphics from the clip art site RetroKat
© 2008 Thomas J Engelsma