Benedict Irwin edited Primality.tex  over 9 years ago

Commit id: b2f6a71983b157f5420bcacf70ed6ddead41b229

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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}