Problems & Puzzles: Puzzles

Puzzle 647. Shifted alphabet rows

For sure you know these games of rows of shifted alphabet lines made in order to discover valid words by columns, for some defined language (BTW, what is the name of these kind of games?).

An example in English for the words "hood" and "zipper":

With this in mind, I have created a parallel numeric puzzle.

Let's define our alphabet as "0123456789" and let's look solutions using exactly ten rows & columns.  Each row may start in any valid "letter" of our alphabet and we may repeat the starting letter in different rows. Of course in every row no letter is repeated, just keep the order by shifting.

Now, in each column we should mark the largest length prime and must add these ten lengths in L.

Just to give a kind of good starting point to beat, I offer this example: Sum of all lengths, L=83

 2 3 4 5 6 7 8 9 0 1 9 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9 7 8 9 0 1 2 3 4 5 6 8 9 0 1 2 3 4 5 6 7 6 7 8 9 0 1 2 3 4 5 9 0 1 2 3 4 5 6 7 8 3 4 5 6 7 8 9 0 1 2 5 6 7 8 9 0 1 2 3 4 4 5 6 7 8 9 0 1 2 3 7 6 9 10 9 10 5 10 7 10 83

Q. Find solutions such that L>83. (Please send just you better solution)

The maximal solution is for L=90 & is unique discarding global shiftings; it was obtained by Giovanni Resta, Ryan Bailey, Emmanuel Vantieghem & Hakan Summakoğlu . This is the solution:

 0 1 2 3 4 5 6 7 8 9 8 9 0 1 2 3 4 5 6 7 7 8 9 0 1 2 3 4 5 6 3 4 5 6 7 8 9 0 1 2 8 9 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 3 4 5 6 7 8 9 0 1 2 2 3 4 5 6 7 8 9 0 1 1 2 3 4 5 6 7 8 9 0 9 9 10 7 8 9 10 9 10 9 90

Claudio Meller sent one solution for L=89.

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