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History of Number of elliptic curves over $\mathbb{Q}$ with good redution outside $S$

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compare when who what
2026-08-13 22:17 bmatschke how well the digits are known: proven (a count of curves, evaluated into an interval field) current
2026-08-13 22:07 bmatschke how well the digits are known: heuristic (a fixed-precision value wrapped in an interval field)
2026-08-09 09:26 label hoist moved the parameter labels onto the parameter they describe
2026-08-09 09:15 flattening entries rewritten as records with named parameters
2026-08-09 08:36 data-repository import attached the files from the data repository reviewed
2026-08-09 08:35 data-repository import the current state of the data repository
2021-05-18 09:59 bmatschke from the data repository, 8da0d7c6
2021-05-17 20:35 bmatschke from the data repository, 61a64fdf
2021-05-17 20:35 bmatschke from the data repository, 63177920
2021-05-17 20:23 bmatschke from the data repository, a91fc211
2021-05-17 20:04 bmatschke from the data repository, ae852ef9

What changed between 2021-05-17 20:23 and 2021-05-17 20:35

from line 19 (5 lines) @@ -19,5 +19,5 @@ 
     by Ogg CITE{Ogg}, $n=2$ by Coghlan CITE{Cog} and Stephens CITE{Ste}, $n=3,4,5$     by von Känel and Matschke CITE{vKanMat} and  Bennett, Gherga and Rechnitzer CITE{BeGhRe},-    $n=6$ heuristically by Best and matschke CITE{BesMat}, $n=7,8,9^*$ by Matschke+    $n=6$ heuristically by Best and Matschke CITE{BesMat}, $n=7,8,9^*$ by Matschke     CITE{M-ECDB} ($n=9$ assumes GRH).' Formulas: {}
from line 74 (5 lines) @@ -74,5 +74,5 @@ 
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         number: '26'   '33':-    param-latex: $\{3, 11\}$+    param_latex: $\{3, 11\}$     numbers:       Q:
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from line 335 (5 lines) @@ -335,5 +335,5 @@ 
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from line 344 (5 lines) @@ -344,5 +344,5 @@ 
         number: '822'   '1155':-    param-latex: $\{3, 5, 7, 11\}$+    param_latex: $\{3, 5, 7, 11\}$     numbers:       Q:
from line 353 (5 lines) @@ -353,5 +353,5 @@ 
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from line 362 (5 lines) @@ -362,5 +362,5 @@ 
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from line 551 (5 lines) @@ -551,5 +551,5 @@ 
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from line 560 (5 lines) @@ -560,5 +560,5 @@ 
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from line 569 (5 lines) @@ -569,5 +569,5 @@ 
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from line 578 (5 lines) @@ -578,5 +578,5 @@ 
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from line 587 (5 lines) @@ -587,5 +587,5 @@ 
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from line 596 (5 lines) @@ -596,5 +596,5 @@ 
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from line 605 (5 lines) @@ -605,5 +605,5 @@ 
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from line 614 (5 lines) @@ -614,5 +614,5 @@ 
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from line 623 (5 lines) @@ -623,5 +623,5 @@ 
         number: '204'   '10010':-    param-latex: $\{2, 5, 7, 11, 13\}$+    param_latex: $\{2, 5, 7, 11, 13\}$     numbers:       Q:
from line 632 (5 lines) @@ -632,5 +632,5 @@ 
         number: '3185'   '15015':-    param-latex: $\{3, 5, 7, 11, 13\}$+    param_latex: $\{3, 5, 7, 11, 13\}$     numbers:       Q:
from line 641 (5 lines) @@ -641,5 +641,5 @@ 
         number: '2294'   '30030':-    param-latex: $\{2, 3, 5, 7, 11, 13\}$+    param_latex: $\{2, 3, 5, 7, 11, 13\}$     numbers:       Q:
from line 650 (5 lines) @@ -650,5 +650,5 @@ 
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from line 659 (5 lines) @@ -659,5 +659,5 @@ 
         number: '4'   '34':-    param-latex: $\{2, 17\}$+    param_latex: $\{2, 17\}$     numbers:       Q:
from line 668 (5 lines) @@ -668,5 +668,5 @@ 
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from line 677 (5 lines) @@ -677,5 +677,5 @@ 
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from line 686 (5 lines) @@ -686,5 +686,5 @@ 
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from line 695 (5 lines) @@ -695,5 +695,5 @@ 
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from line 704 (5 lines) @@ -704,5 +704,5 @@ 
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from line 713 (5 lines) @@ -713,5 +713,5 @@ 
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from line 722 (5 lines) @@ -722,5 +722,5 @@ 
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from line 731 (5 lines) @@ -731,5 +731,5 @@ 
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from line 740 (5 lines) @@ -740,5 +740,5 @@ 
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from line 749 (5 lines) @@ -749,5 +749,5 @@ 
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from line 758 (5 lines) @@ -758,5 +758,5 @@ 
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from line 767 (5 lines) @@ -767,5 +767,5 @@ 
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from line 776 (5 lines) @@ -776,5 +776,5 @@ 
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from line 785 (5 lines) @@ -785,5 +785,5 @@ 
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from line 794 (5 lines) @@ -794,5 +794,5 @@ 
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from line 803 (5 lines) @@ -803,5 +803,5 @@ 
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from line 812 (5 lines) @@ -812,5 +812,5 @@ 
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from line 821 (5 lines) @@ -821,5 +821,5 @@ 
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from line 830 (5 lines) @@ -830,5 +830,5 @@ 
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from line 839 (5 lines) @@ -839,5 +839,5 @@ 
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from line 848 (5 lines) @@ -848,5 +848,5 @@ 
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from line 857 (5 lines) @@ -857,5 +857,5 @@ 
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from line 866 (5 lines) @@ -866,5 +866,5 @@ 
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from line 875 (5 lines) @@ -875,5 +875,5 @@ 
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from line 893 (5 lines) @@ -893,5 +893,5 @@ 
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from line 911 (5 lines) @@ -911,5 +911,5 @@ 
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from line 920 (5 lines) @@ -920,5 +920,5 @@ 
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from line 929 (5 lines) @@ -929,5 +929,5 @@ 
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from line 938 (5 lines) @@ -938,5 +938,5 @@ 
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from line 956 (5 lines) @@ -956,5 +956,5 @@ 
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from line 965 (5 lines) @@ -965,5 +965,5 @@ 
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from line 974 (5 lines) @@ -974,5 +974,5 @@ 
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from line 983 (5 lines) @@ -983,5 +983,5 @@ 
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from line 992 (5 lines) @@ -992,5 +992,5 @@ 
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from line 1019 (5 lines) @@ -1019,5 +1019,5 @@ 
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from line 1028 (5 lines) @@ -1028,5 +1028,5 @@ 
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from line 1037 (5 lines) @@ -1037,5 +1037,5 @@ 
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from line 1046 (5 lines) @@ -1046,5 +1046,5 @@ 
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from line 1055 (5 lines) @@ -1055,5 +1055,5 @@ 
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from line 1064 (5 lines) @@ -1064,5 +1064,5 @@ 
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from line 1073 (5 lines) @@ -1073,5 +1073,5 @@ 
         number: '2040'   '46410':-    param-latex: $\{2, 3, 5, 7, 13, 17\}$+    param_latex: $\{2, 3, 5, 7, 13, 17\}$     numbers:       Q:
from line 1082 (5 lines) @@ -1082,5 +1082,5 @@ 
         number: '31458'   '2431':-    param-latex: $\{11, 13, 17\}$+    param_latex: $\{11, 13, 17\}$     numbers:       Q:
from line 1091 (5 lines) @@ -1091,5 +1091,5 @@ 
         number: '43'   '4862':-    param-latex: $\{2, 11, 13, 17\}$+    param_latex: $\{2, 11, 13, 17\}$     numbers:       Q:
from line 1100 (5 lines) @@ -1100,5 +1100,5 @@ 
         number: '460'   '7293':-    param-latex: $\{3, 11, 13, 17\}$+    param_latex: $\{3, 11, 13, 17\}$     numbers:       Q:
from line 1109 (5 lines) @@ -1109,5 +1109,5 @@ 
         number: '385'   '14586':-    param-latex: $\{2, 3, 11, 13, 17\}$+    param_latex: $\{2, 3, 11, 13, 17\}$     numbers:       Q:
from line 1118 (5 lines) @@ -1118,5 +1118,5 @@ 
         number: '5082'   '12155':-    param-latex: $\{5, 11, 13, 17\}$+    param_latex: $\{5, 11, 13, 17\}$     numbers:       Q:
from line 1127 (5 lines) @@ -1127,5 +1127,5 @@ 
         number: '154'   '24310':-    param-latex: $\{2, 5, 11, 13, 17\}$+    param_latex: $\{2, 5, 11, 13, 17\}$     numbers:       Q:
from line 1136 (5 lines) @@ -1136,5 +1136,5 @@ 
         number: '2566'   '36465':-    param-latex: $\{3, 5, 11, 13, 17\}$+    param_latex: $\{3, 5, 11, 13, 17\}$     numbers:       Q:
from line 1145 (5 lines) @@ -1145,5 +1145,5 @@ 
         number: '1752'   '72930':-    param-latex: $\{2, 3, 5, 11, 13, 17\}$+    param_latex: $\{2, 3, 5, 11, 13, 17\}$     numbers:       Q:
from line 1154 (5 lines) @@ -1154,5 +1154,5 @@ 
         number: '27537'   '17017':-    param-latex: $\{7, 11, 13, 17\}$+    param_latex: $\{7, 11, 13, 17\}$     numbers:       Q:
from line 1163 (5 lines) @@ -1163,5 +1163,5 @@ 
         number: '139'   '34034':-    param-latex: $\{2, 7, 11, 13, 17\}$+    param_latex: $\{2, 7, 11, 13, 17\}$     numbers:       Q:
from line 1172 (5 lines) @@ -1172,5 +1172,5 @@ 
         number: '2121'   '51051':-    param-latex: $\{3, 7, 11, 13, 17\}$+    param_latex: $\{3, 7, 11, 13, 17\}$     numbers:       Q:
from line 1181 (5 lines) @@ -1181,5 +1181,5 @@ 
         number: '1527'   '102102':-    param-latex: $\{2, 3, 7, 11, 13, 17\}$+    param_latex: $\{2, 3, 7, 11, 13, 17\}$     numbers:       Q:
from line 1190 (5 lines) @@ -1190,5 +1190,5 @@ 
         number: '24293'   '85085':-    param-latex: $\{5, 7, 11, 13, 17\}$+    param_latex: $\{5, 7, 11, 13, 17\}$     numbers:       Q:
from line 1199 (5 lines) @@ -1199,5 +1199,5 @@ 
         number: '761'   '170170':-    param-latex: $\{2, 5, 7, 11, 13, 17\}$+    param_latex: $\{2, 5, 7, 11, 13, 17\}$     numbers:       Q:
from line 1208 (5 lines) @@ -1208,5 +1208,5 @@ 
         number: '11493'   '255255':-    param-latex: $\{3, 5, 7, 11, 13, 17\}$+    param_latex: $\{3, 5, 7, 11, 13, 17\}$     numbers:       Q:
from line 1217 (5 lines) @@ -1217,5 +1217,5 @@ 
         number: '8107'   '510510':-    param-latex: $\{2, 3, 5, 7, 11, 13, 17\}$+    param_latex: $\{2, 3, 5, 7, 11, 13, 17\}$     numbers:       Q:
from line 1226 (5 lines) @@ -1226,5 +1226,5 @@ 
         number: '124124'   '19':-    param-latex: $\{19\}$+    param_latex: $\{19\}$     numbers:       Q:
from line 1235 (5 lines) @@ -1235,5 +1235,5 @@ 
         number: '4'   '38':-    param-latex: $\{2, 19\}$+    param_latex: $\{2, 19\}$     numbers:       Q:
from line 1244 (5 lines) @@ -1244,5 +1244,5 @@ 
         number: '39'   '57':-    param-latex: $\{3, 19\}$+    param_latex: $\{3, 19\}$     numbers:       Q:
from line 1253 (5 lines) @@ -1253,5 +1253,5 @@ 
         number: '27'   '114':-    param-latex: $\{2, 3, 19\}$+    param_latex: $\{2, 3, 19\}$     numbers:       Q:
from line 1262 (5 lines) @@ -1262,5 +1262,5 @@ 
         number: '338'   '95':-    param-latex: $\{5, 19\}$+    param_latex: $\{5, 19\}$     numbers:       Q:
from line 1271 (5 lines) @@ -1271,5 +1271,5 @@ 
         number: '10'   '190':-    param-latex: $\{2, 5, 19\}$+    param_latex: $\{2, 5, 19\}$     numbers:       Q:
from line 1280 (5 lines) @@ -1280,5 +1280,5 @@ 
         number: '137'   '285':-    param-latex: $\{3, 5, 19\}$+    param_latex: $\{3, 5, 19\}$     numbers:       Q:
from line 1289 (5 lines) @@ -1289,5 +1289,5 @@ 
         number: '111'   '570':-    param-latex: $\{2, 3, 5, 19\}$+    param_latex: $\{2, 3, 5, 19\}$     numbers:       Q:
from line 1298 (5 lines) @@ -1298,5 +1298,5 @@ 
         number: '1728'   '133':-    param-latex: $\{7, 19\}$+    param_latex: $\{7, 19\}$     numbers:       Q:
from line 1307 (5 lines) @@ -1307,5 +1307,5 @@ 
         number: '8'   '266':-    param-latex: $\{2, 7, 19\}$+    param_latex: $\{2, 7, 19\}$     numbers:       Q:
from line 1316 (5 lines) @@ -1316,5 +1316,5 @@ 
         number: '112'   '399':-    param-latex: $\{3, 7, 19\}$+    param_latex: $\{3, 7, 19\}$     numbers:       Q:
from line 1325 (5 lines) @@ -1325,5 +1325,5 @@ 
         number: '102'   '798':-    param-latex: $\{2, 3, 7, 19\}$+    param_latex: $\{2, 3, 7, 19\}$     numbers:       Q:
from line 1334 (5 lines) @@ -1334,5 +1334,5 @@ 
         number: '1585'   '665':-    param-latex: $\{5, 7, 19\}$+    param_latex: $\{5, 7, 19\}$     numbers:       Q:
from line 1343 (5 lines) @@ -1343,5 +1343,5 @@ 
         number: '51'   '1330':-    param-latex: $\{2, 5, 7, 19\}$+    param_latex: $\{2, 5, 7, 19\}$     numbers:       Q:
from line 1352 (5 lines) @@ -1352,5 +1352,5 @@ 
         number: '754'   '1995':-    param-latex: $\{3, 5, 7, 19\}$+    param_latex: $\{3, 5, 7, 19\}$     numbers:       Q:
from line 1361 (5 lines) @@ -1361,5 +1361,5 @@ 
         number: '468'   '3990':-    param-latex: $\{2, 3, 5, 7, 19\}$+    param_latex: $\{2, 3, 5, 7, 19\}$     numbers:       Q:
from line 1370 (5 lines) @@ -1370,5 +1370,5 @@ 
         number: '7908'   '209':-    param-latex: $\{11, 19\}$+    param_latex: $\{11, 19\}$     numbers:       Q:
from line 1379 (5 lines) @@ -1379,5 +1379,5 @@ 
         number: '14'   '418':-    param-latex: $\{2, 11, 19\}$+    param_latex: $\{2, 11, 19\}$     numbers:       Q:
from line 1388 (5 lines) @@ -1388,5 +1388,5 @@ 
         number: '154'   '627':-    param-latex: $\{3, 11, 19\}$+    param_latex: $\{3, 11, 19\}$     numbers:       Q:
from line 1397 (5 lines) @@ -1397,5 +1397,5 @@ 
         number: '92'   '1254':-    param-latex: $\{2, 3, 11, 19\}$+    param_latex: $\{2, 3, 11, 19\}$     numbers:       Q:
from line 1406 (5 lines) @@ -1406,5 +1406,5 @@ 
         number: '1446'   '1045':-    param-latex: $\{5, 11, 19\}$+    param_latex: $\{5, 11, 19\}$     numbers:       Q:
from line 1415 (5 lines) @@ -1415,5 +1415,5 @@ 
         number: '35'   '2090':-    param-latex: $\{2, 5, 11, 19\}$+    param_latex: $\{2, 5, 11, 19\}$     numbers:       Q:
from line 1424 (5 lines) @@ -1424,5 +1424,5 @@ 
         number: '637'   '3135':-    param-latex: $\{3, 5, 11, 19\}$+    param_latex: $\{3, 5, 11, 19\}$     numbers:       Q:
from line 1433 (5 lines) @@ -1433,5 +1433,5 @@ 
         number: '432'   '6270':-    param-latex: $\{2, 3, 5, 11, 19\}$+    param_latex: $\{2, 3, 5, 11, 19\}$     numbers:       Q:
from line 1442 (5 lines) @@ -1442,5 +1442,5 @@ 
         number: '6939'   '1463':-    param-latex: $\{7, 11, 19\}$+    param_latex: $\{7, 11, 19\}$     numbers:       Q:
from line 1451 (5 lines) @@ -1451,5 +1451,5 @@ 
         number: '37'   '2926':-    param-latex: $\{2, 7, 11, 19\}$+    param_latex: $\{2, 7, 11, 19\}$     numbers:       Q:
from line 1460 (5 lines) @@ -1460,5 +1460,5 @@ 
         number: '552'   '4389':-    param-latex: $\{3, 7, 11, 19\}$+    param_latex: $\{3, 7, 11, 19\}$     numbers:       Q:
from line 1469 (5 lines) @@ -1469,5 +1469,5 @@ 
         number: '396'   '8778':-    param-latex: $\{2, 3, 7, 11, 19\}$+    param_latex: $\{2, 3, 7, 11, 19\}$     numbers:       Q:
from line 1478 (5 lines) @@ -1478,5 +1478,5 @@ 
         number: '6340'   '7315':-    param-latex: $\{5, 7, 11, 19\}$+    param_latex: $\{5, 7, 11, 19\}$     numbers:       Q:
from line 1487 (5 lines) @@ -1487,5 +1487,5 @@ 
         number: '177'   '14630':-    param-latex: $\{2, 5, 7, 11, 19\}$+    param_latex: $\{2, 5, 7, 11, 19\}$     numbers:       Q:
from line 1496 (5 lines) @@ -1496,5 +1496,5 @@ 
         number: '2967'   '21945':-    param-latex: $\{3, 5, 7, 11, 19\}$+    param_latex: $\{3, 5, 7, 11, 19\}$     numbers:       Q:
from line 1505 (5 lines) @@ -1505,5 +1505,5 @@ 
         number: '2062'   '43890':-    param-latex: $\{2, 3, 5, 7, 11, 19\}$+    param_latex: $\{2, 3, 5, 7, 11, 19\}$     numbers:       Q:
from line 1514 (5 lines) @@ -1514,5 +1514,5 @@ 
         number: '32287'   '247':-    param-latex: $\{13, 19\}$+    param_latex: $\{13, 19\}$     numbers:       Q:
from line 1523 (5 lines) @@ -1523,5 +1523,5 @@ 
         number: '4'   '494':-    param-latex: $\{2, 13, 19\}$+    param_latex: $\{2, 13, 19\}$     numbers:       Q:
from line 1532 (5 lines) @@ -1532,5 +1532,5 @@ 
         number: '130'   '741':-    param-latex: $\{3, 13, 19\}$+    param_latex: $\{3, 13, 19\}$     numbers:       Q:
from line 1541 (5 lines) @@ -1541,5 +1541,5 @@ 
         number: '80'   '1482':-    param-latex: $\{2, 3, 13, 19\}$+    param_latex: $\{2, 3, 13, 19\}$     numbers:       Q:
from line 1550 (5 lines) @@ -1550,5 +1550,5 @@ 
         number: '1304'   '1235':-    param-latex: $\{5, 13, 19\}$+    param_latex: $\{5, 13, 19\}$     numbers:       Q:
from line 1559 (5 lines) @@ -1559,5 +1559,5 @@ 
         number: '36'   '2470':-    param-latex: $\{2, 5, 13, 19\}$+    param_latex: $\{2, 5, 13, 19\}$     numbers:       Q:
from line 1568 (5 lines) @@ -1568,5 +1568,5 @@ 
         number: '673'   '3705':-    param-latex: $\{3, 5, 13, 19\}$+    param_latex: $\{3, 5, 13, 19\}$     numbers:       Q:
from line 1577 (5 lines) @@ -1577,5 +1577,5 @@ 
         number: '405'   '7410':-    param-latex: $\{2, 3, 5, 13, 19\}$+    param_latex: $\{2, 3, 5, 13, 19\}$     numbers:       Q:
from line 1586 (5 lines) @@ -1586,5 +1586,5 @@ 
         number: '6737'   '1729':-    param-latex: $\{7, 13, 19\}$+    param_latex: $\{7, 13, 19\}$     numbers:       Q:
from line 1595 (5 lines) @@ -1595,5 +1595,5 @@ 
         number: '30'   '3458':-    param-latex: $\{2, 7, 13, 19\}$+    param_latex: $\{2, 7, 13, 19\}$     numbers:       Q:
from line 1604 (5 lines) @@ -1604,5 +1604,5 @@ 
         number: '537'   '5187':-    param-latex: $\{3, 7, 13, 19\}$+    param_latex: $\{3, 7, 13, 19\}$     numbers:       Q:
from line 1613 (5 lines) @@ -1613,5 +1613,5 @@ 
         number: '390'   '10374':-    param-latex: $\{2, 3, 7, 13, 19\}$+    param_latex: $\{2, 3, 7, 13, 19\}$     numbers:       Q:
from line 1622 (5 lines) @@ -1622,5 +1622,5 @@ 
         number: '5971'   '8645':-    param-latex: $\{5, 7, 13, 19\}$+    param_latex: $\{5, 7, 13, 19\}$     numbers:       Q:
from line 1631 (5 lines) @@ -1631,5 +1631,5 @@ 
         number: '178'   '17290':-    param-latex: $\{2, 5, 7, 13, 19\}$+    param_latex: $\{2, 5, 7, 13, 19\}$     numbers:       Q:
from line 1640 (5 lines) @@ -1640,5 +1640,5 @@ 
         number: '2782'   '25935':-    param-latex: $\{3, 5, 7, 13, 19\}$+    param_latex: $\{3, 5, 7, 13, 19\}$     numbers:       Q:
from line 1649 (5 lines) @@ -1649,5 +1649,5 @@ 
         number: '1956'   '51870':-    param-latex: $\{2, 3, 5, 7, 13, 19\}$+    param_latex: $\{2, 3, 5, 7, 13, 19\}$     numbers:       Q:
from line 1658 (5 lines) @@ -1658,5 +1658,5 @@ 
         number: '31018'   '2717':-    param-latex: $\{11, 13, 19\}$+    param_latex: $\{11, 13, 19\}$     numbers:       Q:
from line 1667 (5 lines) @@ -1667,5 +1667,5 @@ 
         number: '29'   '5434':-    param-latex: $\{2, 11, 13, 19\}$+    param_latex: $\{2, 11, 13, 19\}$     numbers:       Q:
from line 1676 (5 lines) @@ -1676,5 +1676,5 @@ 
         number: '519'   '8151':-    param-latex: $\{3, 11, 13, 19\}$+    param_latex: $\{3, 11, 13, 19\}$     numbers:       Q:
from line 1685 (5 lines) @@ -1685,5 +1685,5 @@ 
         number: '325'   '16302':-    param-latex: $\{2, 3, 11, 13, 19\}$+    param_latex: $\{2, 3, 11, 13, 19\}$     numbers:       Q:
from line 1694 (5 lines) @@ -1694,5 +1694,5 @@ 
         number: '5170'   '13585':-    param-latex: $\{5, 11, 13, 19\}$+    param_latex: $\{5, 11, 13, 19\}$     numbers:       Q:
from line 1703 (5 lines) @@ -1703,5 +1703,5 @@ 
         number: '143'   '27170':-    param-latex: $\{2, 5, 11, 13, 19\}$+    param_latex: $\{2, 5, 11, 13, 19\}$     numbers:       Q:
from line 1712 (5 lines) @@ -1712,5 +1712,5 @@ 
         number: '2559'   '40755':-    param-latex: $\{3, 5, 11, 13, 19\}$+    param_latex: $\{3, 5, 11, 13, 19\}$     numbers:       Q:
from line 1721 (5 lines) @@ -1721,5 +1721,5 @@ 
         number: '1764'   '81510':-    param-latex: $\{2, 3, 5, 11, 13, 19\}$+    param_latex: $\{2, 3, 5, 11, 13, 19\}$     numbers:       Q:
from line 1730 (5 lines) @@ -1730,5 +1730,5 @@ 
         number: '27055'   '19019':-    param-latex: $\{7, 11, 13, 19\}$+    param_latex: $\{7, 11, 13, 19\}$     numbers:       Q:
from line 1739 (5 lines) @@ -1739,5 +1739,5 @@ 
         number: '141'   '38038':-    param-latex: $\{2, 7, 11, 13, 19\}$+    param_latex: $\{2, 7, 11, 13, 19\}$     numbers:       Q:
from line 1748 (5 lines) @@ -1748,5 +1748,5 @@ 
         number: '2091'   '57057':-    param-latex: $\{3, 7, 11, 13, 19\}$+    param_latex: $\{3, 7, 11, 13, 19\}$     numbers:       Q:
from line 1757 (5 lines) @@ -1757,5 +1757,5 @@ 
         number: '1603'   '114114':-    param-latex: $\{2, 3, 7, 11, 13, 19\}$+    param_latex: $\{2, 3, 7, 11, 13, 19\}$     numbers:       Q:
from line 1766 (5 lines) @@ -1766,5 +1766,5 @@ 
         number: '23808'   '95095':-    param-latex: $\{5, 7, 11, 13, 19\}$+    param_latex: $\{5, 7, 11, 13, 19\}$     numbers:       Q:
from line 1775 (5 lines) @@ -1775,5 +1775,5 @@ 
         number: '693'   '190190':-    param-latex: $\{2, 5, 7, 11, 13, 19\}$+    param_latex: $\{2, 5, 7, 11, 13, 19\}$     numbers:       Q:
from line 1784 (5 lines) @@ -1784,5 +1784,5 @@ 
         number: '11036'   '285285':-    param-latex: $\{3, 5, 7, 11, 13, 19\}$+    param_latex: $\{3, 5, 7, 11, 13, 19\}$     numbers:       Q:
from line 1793 (5 lines) @@ -1793,5 +1793,5 @@ 
         number: '7947'   '570570':-    param-latex: $\{2, 3, 5, 7, 11, 13, 19\}$+    param_latex: $\{2, 3, 5, 7, 11, 13, 19\}$     numbers:       Q:
from line 1802 (5 lines) @@ -1802,5 +1802,5 @@ 
         number: '120695'   '323':-    param-latex: $\{17, 19\}$+    param_latex: $\{17, 19\}$     numbers:       Q:
from line 1811 (5 lines) @@ -1811,5 +1811,5 @@ 
         number: '13'   '646':-    param-latex: $\{2, 17, 19\}$+    param_latex: $\{2, 17, 19\}$     numbers:       Q:
from line 1820 (5 lines) @@ -1820,5 +1820,5 @@ 
         number: '123'   '969':-    param-latex: $\{3, 17, 19\}$+    param_latex: $\{3, 17, 19\}$     numbers:       Q:
from line 1829 (5 lines) @@ -1829,5 +1829,5 @@ 
         number: '84'   '1938':-    param-latex: $\{2, 3, 17, 19\}$+    param_latex: $\{2, 3, 17, 19\}$     numbers:       Q:
from line 1838 (5 lines) @@ -1838,5 +1838,5 @@ 
         number: '1265'   '1615':-    param-latex: $\{5, 17, 19\}$+    param_latex: $\{5, 17, 19\}$     numbers:       Q:
from line 1847 (5 lines) @@ -1847,5 +1847,5 @@ 
         number: '42'   '3230':-    param-latex: $\{2, 5, 17, 19\}$+    param_latex: $\{2, 5, 17, 19\}$     numbers:       Q:
from line 1856 (5 lines) @@ -1856,5 +1856,5 @@ 
         number: '626'   '4845':-    param-latex: $\{3, 5, 17, 19\}$+    param_latex: $\{3, 5, 17, 19\}$     numbers:       Q:
from line 1865 (5 lines) @@ -1865,5 +1865,5 @@ 
         number: '399'   '9690':-    param-latex: $\{2, 3, 5, 17, 19\}$+    param_latex: $\{2, 3, 5, 17, 19\}$     numbers:       Q:
from line 1874 (5 lines) @@ -1874,5 +1874,5 @@ 
         number: '6249'   '2261':-    param-latex: $\{7, 17, 19\}$+    param_latex: $\{7, 17, 19\}$     numbers:       Q:
from line 1883 (5 lines) @@ -1883,5 +1883,5 @@ 
         number: '38'   '4522':-    param-latex: $\{2, 7, 17, 19\}$+    param_latex: $\{2, 7, 17, 19\}$     numbers:       Q:
from line 1892 (5 lines) @@ -1892,5 +1892,5 @@ 
         number: '551'   '6783':-    param-latex: $\{3, 7, 17, 19\}$+    param_latex: $\{3, 7, 17, 19\}$     numbers:       Q:
from line 1901 (5 lines) @@ -1901,5 +1901,5 @@ 
         number: '365'   '13566':-    param-latex: $\{2, 3, 7, 17, 19\}$+    param_latex: $\{2, 3, 7, 17, 19\}$     numbers:       Q:
from line 1910 (5 lines) @@ -1910,5 +1910,5 @@ 
         number: '5663'   '11305':-    param-latex: $\{5, 7, 17, 19\}$+    param_latex: $\{5, 7, 17, 19\}$     numbers:       Q:
from line 1919 (5 lines) @@ -1919,5 +1919,5 @@ 
         number: '209'   '22610':-    param-latex: $\{2, 5, 7, 17, 19\}$+    param_latex: $\{2, 5, 7, 17, 19\}$     numbers:       Q:
from line 1928 (5 lines) @@ -1928,5 +1928,5 @@ 
         number: '2750'   '33915':-    param-latex: $\{3, 5, 7, 17, 19\}$+    param_latex: $\{3, 5, 7, 17, 19\}$     numbers:       Q:
from line 1937 (5 lines) @@ -1937,5 +1937,5 @@ 
         number: '1936'   '67830':-    param-latex: $\{2, 3, 5, 7, 17, 19\}$+    param_latex: $\{2, 3, 5, 7, 17, 19\}$     numbers:       Q:
from line 1946 (5 lines) @@ -1946,5 +1946,5 @@ 
         number: '28285'   '3553':-    param-latex: $\{11, 17, 19\}$+    param_latex: $\{11, 17, 19\}$     numbers:       Q:
from line 1955 (5 lines) @@ -1955,5 +1955,5 @@ 
         number: '49'   '7106':-    param-latex: $\{2, 11, 17, 19\}$+    param_latex: $\{2, 11, 17, 19\}$     numbers:       Q:
from line 1964 (5 lines) @@ -1964,5 +1964,5 @@ 
         number: '468'   '10659':-    param-latex: $\{3, 11, 17, 19\}$+    param_latex: $\{3, 11, 17, 19\}$     numbers:       Q:
from line 1973 (5 lines) @@ -1973,5 +1973,5 @@ 
         number: '378'   '21318':-    param-latex: $\{2, 3, 11, 17, 19\}$+    param_latex: $\{2, 3, 11, 17, 19\}$     numbers:       Q:
from line 1982 (5 lines) @@ -1982,5 +1982,5 @@ 
         number: '5233'   '17765':-    param-latex: $\{5, 11, 17, 19\}$+    param_latex: $\{5, 11, 17, 19\}$     numbers:       Q:
from line 1991 (5 lines) @@ -1991,5 +1991,5 @@ 
         number: '165'   '35530':-    param-latex: $\{2, 5, 11, 17, 19\}$+    param_latex: $\{2, 5, 11, 17, 19\}$     numbers:       Q:
from line 2000 (5 lines) @@ -2000,5 +2000,5 @@ 
         number: '2299'   '53295':-    param-latex: $\{3, 5, 11, 17, 19\}$+    param_latex: $\{3, 5, 11, 17, 19\}$     numbers:       Q:
from line 2009 (5 lines) @@ -2009,5 +2009,5 @@ 
         number: '1653'   '106590':-    param-latex: $\{2, 3, 5, 11, 17, 19\}$+    param_latex: $\{2, 3, 5, 11, 17, 19\}$     numbers:       Q:
from line 2018 (5 lines) @@ -2018,5 +2018,5 @@ 
         number: '25012'   '24871':-    param-latex: $\{7, 11, 17, 19\}$+    param_latex: $\{7, 11, 17, 19\}$     numbers:       Q:
from line 2027 (5 lines) @@ -2027,5 +2027,5 @@ 
         number: '150'   '49742':-    param-latex: $\{2, 7, 11, 17, 19\}$+    param_latex: $\{2, 7, 11, 17, 19\}$     numbers:       Q:
from line 2036 (5 lines) @@ -2036,5 +2036,5 @@ 
         number: '2128'   '74613':-    param-latex: $\{3, 7, 11, 17, 19\}$+    param_latex: $\{3, 7, 11, 17, 19\}$     numbers:       Q:
from line 2045 (5 lines) @@ -2045,5 +2045,5 @@ 
         number: '1555'   '149226':-    param-latex: $\{2, 3, 7, 11, 17, 19\}$+    param_latex: $\{2, 3, 7, 11, 17, 19\}$     numbers:       Q:
from line 2054 (5 lines) @@ -2054,5 +2054,5 @@ 
         number: '22239'   '124355':-    param-latex: $\{5, 7, 11, 17, 19\}$+    param_latex: $\{5, 7, 11, 17, 19\}$     numbers:       Q:
from line 2063 (5 lines) @@ -2063,5 +2063,5 @@ 
         number: '736'   '248710':-    param-latex: $\{2, 5, 7, 11, 17, 19\}$+    param_latex: $\{2, 5, 7, 11, 17, 19\}$     numbers:       Q:
from line 2072 (5 lines) @@ -2072,5 +2072,5 @@ 
         number: '10457'   '373065':-    param-latex: $\{3, 5, 7, 11, 17, 19\}$+    param_latex: $\{3, 5, 7, 11, 17, 19\}$     numbers:       Q:
from line 2081 (5 lines) @@ -2081,5 +2081,5 @@ 
         number: '7533'   '746130':-    param-latex: $\{2, 3, 5, 7, 11, 17, 19\}$+    param_latex: $\{2, 3, 5, 7, 11, 17, 19\}$     numbers:       Q:
from line 2090 (5 lines) @@ -2090,5 +2090,5 @@ 
         number: '112361'   '4199':-    param-latex: $\{13, 17, 19\}$+    param_latex: $\{13, 17, 19\}$     numbers:       Q:
from line 2099 (5 lines) @@ -2099,5 +2099,5 @@ 
         number: '26'   '8398':-    param-latex: $\{2, 13, 17, 19\}$+    param_latex: $\{2, 13, 17, 19\}$     numbers:       Q:
from line 2108 (5 lines) @@ -2108,5 +2108,5 @@ 
         number: '416'   '12597':-    param-latex: $\{3, 13, 17, 19\}$+    param_latex: $\{3, 13, 17, 19\}$     numbers:       Q:
from line 2117 (5 lines) @@ -2117,5 +2117,5 @@ 
         number: '298'   '25194':-    param-latex: $\{2, 3, 13, 17, 19\}$+    param_latex: $\{2, 3, 13, 17, 19\}$     numbers:       Q:
from line 2126 (5 lines) @@ -2126,5 +2126,5 @@ 
         number: '4927'   '20995':-    param-latex: $\{5, 13, 17, 19\}$+    param_latex: $\{5, 13, 17, 19\}$     numbers:       Q:
from line 2135 (5 lines) @@ -2135,5 +2135,5 @@ 
         number: '130'   '41990':-    param-latex: $\{2, 5, 13, 17, 19\}$+    param_latex: $\{2, 5, 13, 17, 19\}$     numbers:       Q:
from line 2144 (5 lines) @@ -2144,5 +2144,5 @@ 
         number: '2265'   '62985':-    param-latex: $\{3, 5, 13, 17, 19\}$+    param_latex: $\{3, 5, 13, 17, 19\}$     numbers:       Q:
from line 2153 (5 lines) @@ -2153,5 +2153,5 @@ 
         number: '1441'   '125970':-    param-latex: $\{2, 3, 5, 13, 17, 19\}$+    param_latex: $\{2, 3, 5, 13, 17, 19\}$     numbers:       Q:
from line 2162 (5 lines) @@ -2162,5 +2162,5 @@ 
         number: '23809'   '29393':-    param-latex: $\{7, 13, 17, 19\}$+    param_latex: $\{7, 13, 17, 19\}$     numbers:       Q:
from line 2171 (5 lines) @@ -2171,5 +2171,5 @@ 
         number: '116'   '58786':-    param-latex: $\{2, 7, 13, 17, 19\}$+    param_latex: $\{2, 7, 13, 17, 19\}$     numbers:       Q:
from line 2180 (5 lines) @@ -2180,5 +2180,5 @@ 
         number: '1996'   '88179':-    param-latex: $\{3, 7, 13, 17, 19\}$+    param_latex: $\{3, 7, 13, 17, 19\}$     numbers:       Q:
from line 2189 (5 lines) @@ -2189,5 +2189,5 @@ 
         number: '1346'   '176358':-    param-latex: $\{2, 3, 7, 13, 17, 19\}$+    param_latex: $\{2, 3, 7, 13, 17, 19\}$     numbers:       Q:
from line 2198 (5 lines) @@ -2198,5 +2198,5 @@ 
         number: '21111'   '146965':-    param-latex: $\{5, 7, 13, 17, 19\}$+    param_latex: $\{5, 7, 13, 17, 19\}$     numbers:       Q:
from line 2207 (5 lines) @@ -2207,5 +2207,5 @@ 
         number: '705'   '293930':-    param-latex: $\{2, 5, 7, 13, 17, 19\}$+    param_latex: $\{2, 5, 7, 13, 17, 19\}$     numbers:       Q:
from line 2216 (5 lines) @@ -2216,5 +2216,5 @@ 
         number: '10038'   '440895':-    param-latex: $\{3, 5, 7, 13, 17, 19\}$+    param_latex: $\{3, 5, 7, 13, 17, 19\}$     numbers:       Q:
from line 2225 (5 lines) @@ -2225,5 +2225,5 @@ 
         number: '7034'   '881790':-    param-latex: $\{2, 3, 5, 7, 13, 17, 19\}$+    param_latex: $\{2, 3, 5, 7, 13, 17, 19\}$     numbers:       Q:
from line 2234 (5 lines) @@ -2234,5 +2234,5 @@ 
         number: '107612'   '46189':-    param-latex: $\{11, 13, 17, 19\}$+    param_latex: $\{11, 13, 17, 19\}$     numbers:       Q:
from line 2243 (5 lines) @@ -2243,5 +2243,5 @@ 
         number: '122'   '92378':-    param-latex: $\{2, 11, 13, 17, 19\}$+    param_latex: $\{2, 11, 13, 17, 19\}$     numbers:       Q:
from line 2252 (5 lines) @@ -2252,5 +2252,5 @@ 
         number: '1715'   '138567':-    param-latex: $\{3, 11, 13, 17, 19\}$+    param_latex: $\{3, 11, 13, 17, 19\}$     numbers:       Q:
from line 2261 (5 lines) @@ -2261,5 +2261,5 @@ 
         number: '1281'   '277134':-    param-latex: $\{2, 3, 11, 13, 17, 19\}$+    param_latex: $\{2, 3, 11, 13, 17, 19\}$     numbers:       Q:
from line 2270 (5 lines) @@ -2270,5 +2270,5 @@ 
         number: '18719'   '230945':-    param-latex: $\{5, 11, 13, 17, 19\}$+    param_latex: $\{5, 11, 13, 17, 19\}$     numbers:       Q:
from line 2279 (5 lines) @@ -2279,5 +2279,5 @@ 
         number: '529'   '461890':-    param-latex: $\{2, 5, 11, 13, 17, 19\}$+    param_latex: $\{2, 5, 11, 13, 17, 19\}$     numbers:       Q:
from line 2288 (5 lines) @@ -2288,5 +2288,5 @@ 
         number: '8777'   '692835':-    param-latex: $\{3, 5, 11, 13, 17, 19\}$+    param_latex: $\{3, 5, 11, 13, 17, 19\}$     numbers:       Q:
from line 2297 (5 lines) @@ -2297,5 +2297,5 @@ 
         number: '6193'   '1385670':-    param-latex: $\{2, 3, 5, 11, 13, 17, 19\}$+    param_latex: $\{2, 3, 5, 11, 13, 17, 19\}$     numbers:       Q:
from line 2306 (5 lines) @@ -2306,5 +2306,5 @@ 
         number: '93964'   '323323':-    param-latex: $\{7, 11, 13, 17, 19\}$+    param_latex: $\{7, 11, 13, 17, 19\}$     numbers:       Q:
from line 2315 (5 lines) @@ -2315,5 +2315,5 @@ 
         number: '536'   '646646':-    param-latex: $\{2, 7, 11, 13, 17, 19\}$+    param_latex: $\{2, 7, 11, 13, 17, 19\}$     numbers:       Q:
from line 2324 (5 lines) @@ -2324,5 +2324,5 @@ 
         number: '7924'   '969969':-    param-latex: $\{3, 7, 11, 13, 17, 19\}$+    param_latex: $\{3, 7, 11, 13, 17, 19\}$     numbers:       Q:
from line 2333 (5 lines) @@ -2333,5 +2333,5 @@ 
         number: '5792'   '1939938':-    param-latex: $\{2, 3, 7, 11, 13, 17, 19\}$+    param_latex: $\{2, 3, 7, 11, 13, 17, 19\}$     numbers:       Q:
from line 2342 (5 lines) @@ -2342,5 +2342,5 @@ 
         number: '84331'   '1616615':-    param-latex: $\{5, 7, 11, 13, 17, 19\}$+    param_latex: $\{5, 7, 11, 13, 17, 19\}$     numbers:       Q:
from line 2351 (5 lines) @@ -2351,5 +2351,5 @@ 
         number: '2621'   '3233230':-    param-latex: $\{2, 5, 7, 11, 13, 17, 19\}$+    param_latex: $\{2, 5, 7, 11, 13, 17, 19\}$     numbers:       Q:
from line 2360 (5 lines) @@ -2360,5 +2360,5 @@ 
         number: '38967'   '4849845':-    param-latex: $\{3, 5, 7, 11, 13, 17, 19\}$+    param_latex: $\{3, 5, 7, 11, 13, 17, 19\}$     numbers:       Q:
from line 2369 (5 lines) @@ -2369,5 +2369,5 @@ 
         number: '27792'   '9699690':-    param-latex: $\{2, 3, 5, 7, 11, 13, 17, 19\}$+    param_latex: $\{2, 3, 5, 7, 11, 13, 17, 19\}$     numbers:       Q:

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