
theorem
  5987 is prime
proof
  now
    5987 = 2*2993 + 1; hence not 2 divides 5987 by NAT_4:9;
    5987 = 3*1995 + 2; hence not 3 divides 5987 by NAT_4:9;
    5987 = 5*1197 + 2; hence not 5 divides 5987 by NAT_4:9;
    5987 = 7*855 + 2; hence not 7 divides 5987 by NAT_4:9;
    5987 = 11*544 + 3; hence not 11 divides 5987 by NAT_4:9;
    5987 = 13*460 + 7; hence not 13 divides 5987 by NAT_4:9;
    5987 = 17*352 + 3; hence not 17 divides 5987 by NAT_4:9;
    5987 = 19*315 + 2; hence not 19 divides 5987 by NAT_4:9;
    5987 = 23*260 + 7; hence not 23 divides 5987 by NAT_4:9;
    5987 = 29*206 + 13; hence not 29 divides 5987 by NAT_4:9;
    5987 = 31*193 + 4; hence not 31 divides 5987 by NAT_4:9;
    5987 = 37*161 + 30; hence not 37 divides 5987 by NAT_4:9;
    5987 = 41*146 + 1; hence not 41 divides 5987 by NAT_4:9;
    5987 = 43*139 + 10; hence not 43 divides 5987 by NAT_4:9;
    5987 = 47*127 + 18; hence not 47 divides 5987 by NAT_4:9;
    5987 = 53*112 + 51; hence not 53 divides 5987 by NAT_4:9;
    5987 = 59*101 + 28; hence not 59 divides 5987 by NAT_4:9;
    5987 = 61*98 + 9; hence not 61 divides 5987 by NAT_4:9;
    5987 = 67*89 + 24; hence not 67 divides 5987 by NAT_4:9;
    5987 = 71*84 + 23; hence not 71 divides 5987 by NAT_4:9;
    5987 = 73*82 + 1; hence not 73 divides 5987 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5987 & n is prime
  holds not n divides 5987 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
