Benedict Irwin edited The 90 Thing.tex  over 9 years ago

Commit id: 83f1999962d8d978444ff23f97b402682248d8f3

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\hline  n & prime? & num & fac\\  0 & 0 & 1 & 1 \\  1 & 0 & 91 & 7×13\\%Failed  2 & 1 & (90;2)+1 & (90;2)+1 \\  3 & 1 & (90;3)+1 & (90;3)+1 \\  4 & 0 & ... & 7×13×19×52579 \\  5 & 0 & ... & 11×23×4093×8779 \\%Failed  6 & 0 & ... & 859×1058313049 \\%Failed  7 & 0 & ... & 7×13×211×241×2161×9091 \\  8 & 0 & ... & 103×4013×21993833369 \\%Failed  9 & 1 & (90;9)+1 & (90;9)+1 \\  10 & 0 & ... & 7^2×13×127×2689×459691×909091 \\  11 & 0 & ... & 47×139×2531×549797184491917 \\%Failed  12 & 0 & ... & 251×5051×9091×78875943472201 \\  13 & 0 & ... & 7×13×19×52579×70541929×14175966169 \\  14 & 0 & ... & 59×154083204930662557781201849 \\%Failed  15 & 1 & (90;15)+1 & (90;15)+1 \\  16 & 0 & ... & 7×11×13×23×4093×8779×599144041×183411838171 \\  17 & 0 & ... & 9091×909091×4147571×265212793249617641 \\  18 & 0 & ... & 7253×422650073734453×296557347313446299 \\%Failed  19 & 0 & ... & 7×13^2×157×859×6397×216451×1058313049×388847808493 \\  20 & 0 & ... & 2670502781396266997×3404193829806058997303 \\%Failed  21 & 0 & ... & 57009401×2182600451×7306116556571817748755241 \\%Failed  22 & 0 & ... & 7×13×19×211×241×2161×9091×29611×52579×3762091×8985695684401 \\  \end{array}  \end{equation} 

This is cute, as instead of cheking a number a billion digits long, we can check a number log_{10}(digits) in a linear way.  \section{Improving the algorithm...} algorithm}  So from the table above in the first $22$ concatenations, we can see $2,3,9,15,...$ are prime.  Of course in the spirit of OEIS: we have $A054416$ which will continues that sequence for a little longer as 2, 3, 9, 15, 26, 33, 146, 320, 1068, 1505...