this is for holding javascript data
Benedict Irwin edited Primality.tex
over 9 years ago
Commit id: b2f6a71983b157f5420bcacf70ed6ddead41b229
deletions | additions
diff --git a/Primality.tex b/Primality.tex
index a27de64..497e1b8 100644
--- a/Primality.tex
+++ b/Primality.tex
...
1;40 & 0 & 11×41×73×101×137×271×3541×9091×27961×1676321×5964848081 \\
1;41 & 0 & 83×1231×538987×201763709900322803748657942361 \\
1;42 & 0 & 3×7^2×11×13×37×43×127×239×1933×2689×4649×459691×909091×10838689 \\
1;43 & 0 & 173×1527791×1963506722254397×2140992015395526641\\
1;44 & 0 & 11^2×23×89×101×4093×8779×21649×513239×1052788969×1056689261 \\
1;45 & 0 & 3^2×31×37×41×271×238681×333667×2906161×4185502830133110721 \\
1;46 & 0 & 11×47×139×2531×549797184491917×11111111111111111111111 \\
1;47 & 0 & 35121409×316362908763458525001406154038726382279 \\
1;48 & 0 & 3×7×11×13×17×37×73×101×137×9901×5882353×99990001×9999999900000001 \\
1;49 & 0 & 239×4649×505885997×1976730144598190963568023014679333 \\
1;50 & 0 & 11×41×251×271×5051×9091×21401×25601×182521213001×78875943472201 \\
\end{array}
\end{equation}
Finding sequences of $901$ components
\begin{equation}
\begin{array}{|c|c|c|}
\hline
& prime & rep \\
\hline
1;1 & 0 & 1 \\
1;2 & 1 & 11 \\
1;3 & 0 & 3×37 \\
1;4 & 0 & 11×101 \\
1;5 & 0 & 41×271 \\
1;6 & 91 & 3×7×11×13×37 \\
1;7 & 0 & 239×4649 \\
1;8 & 0 & 11×73×101×137 \\
1;9 & 0 & 3^2×37×333667 \\
1;10 & 9091 & 11×41×271×9091 \\
1;11 & 0 & 21649×513239 \\
1;12 & 91,9901 & 3×7×11×13×37×101×9901 \\
1;13 & 0 & 53×79×265371653 \\
1;14 & 909091 & 11×239×4649×909091 \\
1;15 & 0 & 3×31×37×41×271×2906161 \\
1;16 & 0 & 11×17×73×101×137×5882353 \\
1;17 & 0 & 2071723×5363222357 \\
1;18 & 91,999001 & 3^2×7×11×13×19×37×52579×333667 \\
1;19 & 1 & 1;19 \\
1;20 & 9091,99009901 & 11×41×101×271×3541×9091×27961 \\
1;21 & 0 & 3×37×43×239×1933×4649×10838689 \\
1;22 & 0 & 11^2×23×4093×8779×21649×513239 \\
1;23 & 1 & 1;23 \\
1;24 & 91,9901,99990001 & 3×7×11×13×37×73×101×137×9901×99990001 \\
1;25 & 0 & 41×271×21401×25601×182521213001 \\
1;26 & 0 & 11×53×79×859×265371653×1058313049 \\
1;27 & 0 & 3^3×37×757×333667×440334654777631 \\
1;28 & 909091 & 11×29×101×239×281×4649×909091×121499449 \\
1;29 & 0 & 3191×16763×43037×62003×77843839397 \\
1;30 & 91,9091,9999900001,999000999001 & 3×7×11×13×31×37×41×211×241×271×2161×9091×2906161 \\
1;31 & 0 & 2791×6943319×57336415063790604359 \\
1;32 & 0 & 11×17×73×101×137×353×449×641×1409×69857×5882353 \\
1;33 & 0 & 3×37×67×21649×513239×1344628210313298373 \\
1;34 & 0 & 11×103×4013×2071723×5363222357×21993833369 \\
1;35 & 0 & 41×71×239×271×4649×123551×102598800232111471 \\
1;36 & 91,9901,999001,999999000001 & 3^2×7×11×13×19×37×101×9901×52579×333667×999999000001 \\
1;37 & 0 & 2028119×247629013×2212394296770203368013 \\
1;38 & 909090909090909091 & 11×909090909090909091×1111111111111111111 \\
1;39 & 900900900900990990990991 & 3×37×53×79×265371653×900900900900990990990991 \\
1;40 & 9091,99009901 & 11×41×73×101×137×271×3541×9091×27961×1676321×5964848081 \\
1;41 & 0 & 83×1231×538987×201763709900322803748657942361 \\
1;42 & 91,909091 & 3×7^2×11×13×37×43×127×239×1933×2689×4649×459691×909091×10838689 \\
1;43 & 0 & 173×1527791×1963506722254397×2140992015395526641\\
1;44 & 0 & 11^2×23×89×101×4093×8779×21649×513239×1052788969×1056689261 \\
1;45 & 0 & 3^2×31×37×41×271×238681×333667×2906161×4185502830133110721 \\
1;46 & 0 & 11×47×139×2531×549797184491917×11111111111111111111111 \\
1;47 & 0 & 35121409×316362908763458525001406154038726382279 \\
1;48 & 91,9901,99990001,9999999900000001 & 3×7×11×13×17×37×73×101×137×9901×5882353×99990001×9999999900000001 \\
1;49 & 0 & 239×4649×505885997×1976730144598190963568023014679333 \\
1;50 & 9091 & 11×41×251×271×5051×9091×21401×25601×182521213001×78875943472201 \\
\end{array}
\end{equation}
The second column above is the possibility to form the sequence.
Some of the prime factors needed will overlap. But this gives a divisibility by check.
Consider, the "squared" [not under multiplication some other operation] of a prime... leading to another, some kind of sequence combination/manipulation/convolution.
Divisors of $n$ and prime divisors of $1;n$ comparison table.
\begin{equation}