Selecting elements in nested list

Question

I want to compare elements in a list that looks like this

{{{4, 1}}, {{1, 2}}, {{1, 3}}, {{2, 4}}, {{2, 5}}, {{2, 6}}, {{1, 
7}}, {{4, 8}}, {{1, 9}}, {{4, 10}}, {{2, 11}}, {{4, 12}}, {{4, 
13}}, {{2, 14}}, {{2, 15}}, {{1, 16}}, {{4, 17}}, {{2, 18}}, {{2, 
19}}, {{1, 20}}, {{1, 21}}, {{4, 22}}, {{4, 23}}, {{1, 24}}, {{2, 
25}}, {{1, 26}}, {{4, 27}}, {{4, 28}}, {{4, 29}}, {{4, 30}},.....

I want to select the smalest (first) number b in the pair {a,b} where a will be greater than 4.

Answer 1

I added two entries with a > 4:

data = {{{4, 1}}, {{1, 2}}, {{1, 3}}, {{2, 4}}, {{2, 5}}, {{2, 6}}, {{1, 7}},
   {{5, 123}},
   {{4, 8}}, {{1, 9}}, {{4, 10}}, {{2, 11}}, {{4, 12}}, {{4, 13}}, {{2, 14}},
   {{6, 456}},
   {{2, 15}}, {{1, 16}}, {{4, 17}}, {{2, 18}}, {{2, 19}}, {{1, 20}}, {{1, 21}},
   {{4, 22}}, {{4, 23}}, {{1, 24}}, {{2, 25}}, {{1, 26}}, {{4, 27}}, {{4, 28}},
   {{4, 29}}, {{4, 30}}};

Then are several options (uncomment First to get the number by itself):

(*First@*) Cases[data, {{a_, b_}} /; a > 4 :> b, 1, 1]
(*  {123}  *)

A couple more:

FirstCase[data, {{a_, b_}} /; a > 4 :> b]
Select[data, #[[1, 1]] > 4 &, 1][[1, 1, 2]]
(*  123  *)

Answer 2

Here's my go

Elements:

x = Table[RandomInteger[30], 10, 2]

x={{4,6},{0,7},{0,2},{12,9},{2,19},{28,6},{10,12},{19,4},{30,29},{19,5}}

SelectFirst[SortBy[x, #[[2]] &], #[[1]] > 4 &]

Which gives {19,4}

Wasn't too sure, hopefully this meets the condition of "First smallest 'b'"