now :: thesis: ( not 2 divides 211 & not 3 divides 211 & not 5 divides 211 & not 7 divides 211 & not 11 divides 211 & not 13 divides 211 )

211 = (2 * 105) + 1 ;
hence not 2 divides 211 by NAT_4:9; :: thesis: ( not 3 divides 211 & not 5 divides 211 & not 7 divides 211 & not 11 divides 211 & not 13 divides 211 )
211 = (3 * 70) + 1 ;
hence not 3 divides 211 by NAT_4:9; :: thesis: ( not 5 divides 211 & not 7 divides 211 & not 11 divides 211 & not 13 divides 211 )
211 = (5 * 42) + 1 ;
hence not 5 divides 211 by NAT_4:9; :: thesis: ( not 7 divides 211 & not 11 divides 211 & not 13 divides 211 )
211 = (7 * 30) + 1 ;
hence not 7 divides 211 by NAT_4:9; :: thesis: ( not 11 divides 211 & not 13 divides 211 )
211 = (11 * 19) + 2 ;
hence not 11 divides 211 by NAT_4:9; :: thesis: not 13 divides 211
211 = (13 * 16) + 3 ;
hence not 13 divides 211 by NAT_4:9; :: thesis: verum

end;

then for n being Element of NAT st 1 < n & n * n <= 211 & n is prime holds
not n divides 211 by XPRIMET1:12;
hence 211 is prime by NAT_4:14; :: thesis: verum