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This is a follow-on from a similar question here. If I already have a table of data, say

table1 = {{0, 0, 0, 0, 0, 0}, 
 {0, 1, 2, 3, 4, 5}, 
 {0, 2, 4, 6, 8, 10}, 
 {0, 3, 6, 9, 12, 15}, 
 {0, 4, 8, 12, 16, 20}, 
 {0, 5, 10, 15, 20, 25}, 
 {0, 6, 12, 18, 24, 30}, 
 {0, 7, 14, 21, 28, 35}, 
 {0, 8, 16, 24, 32, 40}, 
 {0, 9, 18, 27, 36, 45}, 
 {0, 10, 20, 30, 40, 50}, 
 {0, 11, 22, 33, 44, 55}, 
 {0, 12, 24, 36, 48, 60}, 
 {0, 13, 26, 39, 52, 65}, 
 {0, 14, 28, 42, 56, 70}, 
 {0, 15, 30, 45, 60, 75}}

and I want to present this in TableForm with the rows whose row numbers are prime (i.e., rows 2,3,5...) in bold, how do I do this by applying functions to table1? Perhaps some combination of If, Length, Range and PrimeQ?

Obviously in the above case the table is small enough to do it manually, but I want to be able to do this with any arbitrary pre-existing table of data.

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5 Answers 5

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Does something like this do what you want?

table1 /. (row : {a_?NumberQ, b_?PrimeQ, c___?NumberQ} :>Map[Highlighted@Style[#, Bold] &, row]) // TableForm  

Hi Richard. Not sure I fully understand what you're trying to achieve, so the following suggestions are a bit of a guess.

table1[[All, 2]] += 1; 
table1 /. (row : {a_?NumberQ, b_?PrimeQ, c___?NumberQ} :> 
Map[Highlighted@Style[#, Bold] &, row]) // TableForm

All I've done here is modify your table1 to add a 'shift' value of 1 to all values in the second column. If you want to leave table1 as-is, you could try the following.

table1 /. (row : {a_?NumberQ, b_?NumberQ, c___?NumberQ} :> 
Map[Highlighted@Style[#, Bold] &, row] /; 
 PrimeQ[b + 1]) // TableForm

This code imposes a condition such that the rewrite rule is invoked only if the value of the number in the second column when added to 1 is Prime.

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  • $\begingroup$ One additional request - should have made this clearer... What if there's an offset? Like if the first row is actually row 0 instead of row 1? Which bit do I change? $\endgroup$ Mar 28, 2019 at 11:39
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Grid has flexible formatting options for table items compared to TableForm. The syntax is also cleaner.

table1 = {{0, 0, 0, 0, 0, 0}, {0, 1, 2, 3, 4, 5}, {0, 2, 4, 6, 8, 
    10}, {0, 3, 6, 9, 12, 15}, {0, 4, 8, 12, 16, 20}, {0, 5, 10, 15, 
    20, 25}, {0, 6, 12, 18, 24, 30}, {0, 7, 14, 21, 28, 35}, {0, 8, 
    16, 24, 32, 40}, {0, 9, 18, 27, 36, 45}, {0, 10, 20, 30, 40, 
    50}, {0, 11, 22, 33, 44, 55}, {0, 12, 24, 36, 48, 60}, {0, 13, 26,
     39, 52, 65}, {0, 14, 28, 42, 56, 70}, {0, 15, 30, 45, 60, 75}};


rows = Flatten@Position[table1[[All, 2]], _?PrimeQ];
s1 = Thread[rows -> Directive[Bold, Black]];
b2 = Thread[rows -> Lighter@Cyan];
b3 = {{9, 11}, {2, 4}} -> Lighter@Yellow;

Grid[table1
 , Background -> {None, b2, b3}
 , ItemStyle -> {Automatic, s1 }
 , Frame -> {None, None, {{9, 11}, {2, 4}} -> Directive[Red]}
 ]

enter image description here

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list = 
 {{0, 0, 0, 0, 0, 0}, 
 {0, 1, 2, 3, 4, 5}, 
 {0, 2, 4, 6, 8, 10}, 
 {0, 3, 6, 9, 12, 15}, 
 {0, 4, 8, 12, 16, 20}, 
 {0, 5, 10, 15, 20, 25}, 
 {0, 6, 12, 18, 24, 30}, 
 {0, 7, 14, 21, 28, 35}, 
 {0, 8, 16, 24, 32, 40}, 
 {0, 9, 18, 27, 36, 45}, 
 {0, 10, 20, 30, 40, 50}, 
 {0, 11, 22, 33, 44, 55}, 
 {0, 12, 24, 36, 48, 60}, 
 {0, 13, 26, 39, 52, 65}, 
 {0, 14, 28, 42, 56, 70}, 
 {0, 15, 30, 45, 60, 75}}

Get positions of primes in 2nd column with appended All

p = Append[All] /@ Position[list, {_, _?PrimeQ, __}]

{{3, All}, {4, All}, {6, All}, {8, All}, {12, All}, {14, All}}

Using ReplaceAt (new in 13.1)

ReplaceAt[a_ :> Style[a, Bold], p] @ list // TableForm

enter image description here

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Dataset[table1, 
 ItemStyle -> _?(PrimeQ[# - 1] &) -> Bold, 
 Background -> (If[PrimeQ[#2[[1]] - 1], Cyan, White] &)]

enter image description here

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Since "row number" is not clearly specified in the OP, here I just assume that the first row ({0, 0, 0, 0, 0, 0}) has row number 1.

Using MapIndexed:

ClearAll[style]
style[list_List, {n_}] /; PrimeQ[n] := Style[#, Bold] & /@ list
style[list_List, {n_}] := list

MapIndexed[style, table1] // TableForm

or MapAt

MapAt[Style[#, Bold] &, table1, 
  Table[{Prime[row], All}, {row, 1, 
    PrimePi[Length@table1]}]] // TableForm

enter image description here

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