
theorem
  9973 is prime
proof
  now
    9973 = 2*4986 + 1; hence not 2 divides 9973 by NAT_4:9;
    9973 = 3*3324 + 1; hence not 3 divides 9973 by NAT_4:9;
    9973 = 5*1994 + 3; hence not 5 divides 9973 by NAT_4:9;
    9973 = 7*1424 + 5; hence not 7 divides 9973 by NAT_4:9;
    9973 = 11*906 + 7; hence not 11 divides 9973 by NAT_4:9;
    9973 = 13*767 + 2; hence not 13 divides 9973 by NAT_4:9;
    9973 = 17*586 + 11; hence not 17 divides 9973 by NAT_4:9;
    9973 = 19*524 + 17; hence not 19 divides 9973 by NAT_4:9;
    9973 = 23*433 + 14; hence not 23 divides 9973 by NAT_4:9;
    9973 = 29*343 + 26; hence not 29 divides 9973 by NAT_4:9;
    9973 = 31*321 + 22; hence not 31 divides 9973 by NAT_4:9;
    9973 = 37*269 + 20; hence not 37 divides 9973 by NAT_4:9;
    9973 = 41*243 + 10; hence not 41 divides 9973 by NAT_4:9;
    9973 = 43*231 + 40; hence not 43 divides 9973 by NAT_4:9;
    9973 = 47*212 + 9; hence not 47 divides 9973 by NAT_4:9;
    9973 = 53*188 + 9; hence not 53 divides 9973 by NAT_4:9;
    9973 = 59*169 + 2; hence not 59 divides 9973 by NAT_4:9;
    9973 = 61*163 + 30; hence not 61 divides 9973 by NAT_4:9;
    9973 = 67*148 + 57; hence not 67 divides 9973 by NAT_4:9;
    9973 = 71*140 + 33; hence not 71 divides 9973 by NAT_4:9;
    9973 = 73*136 + 45; hence not 73 divides 9973 by NAT_4:9;
    9973 = 79*126 + 19; hence not 79 divides 9973 by NAT_4:9;
    9973 = 83*120 + 13; hence not 83 divides 9973 by NAT_4:9;
    9973 = 89*112 + 5; hence not 89 divides 9973 by NAT_4:9;
    9973 = 97*102 + 79; hence not 97 divides 9973 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9973 & n is prime
  holds not n divides 9973 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
