
theorem
  9187 is prime
proof
  now
    9187 = 2*4593 + 1; hence not 2 divides 9187 by NAT_4:9;
    9187 = 3*3062 + 1; hence not 3 divides 9187 by NAT_4:9;
    9187 = 5*1837 + 2; hence not 5 divides 9187 by NAT_4:9;
    9187 = 7*1312 + 3; hence not 7 divides 9187 by NAT_4:9;
    9187 = 11*835 + 2; hence not 11 divides 9187 by NAT_4:9;
    9187 = 13*706 + 9; hence not 13 divides 9187 by NAT_4:9;
    9187 = 17*540 + 7; hence not 17 divides 9187 by NAT_4:9;
    9187 = 19*483 + 10; hence not 19 divides 9187 by NAT_4:9;
    9187 = 23*399 + 10; hence not 23 divides 9187 by NAT_4:9;
    9187 = 29*316 + 23; hence not 29 divides 9187 by NAT_4:9;
    9187 = 31*296 + 11; hence not 31 divides 9187 by NAT_4:9;
    9187 = 37*248 + 11; hence not 37 divides 9187 by NAT_4:9;
    9187 = 41*224 + 3; hence not 41 divides 9187 by NAT_4:9;
    9187 = 43*213 + 28; hence not 43 divides 9187 by NAT_4:9;
    9187 = 47*195 + 22; hence not 47 divides 9187 by NAT_4:9;
    9187 = 53*173 + 18; hence not 53 divides 9187 by NAT_4:9;
    9187 = 59*155 + 42; hence not 59 divides 9187 by NAT_4:9;
    9187 = 61*150 + 37; hence not 61 divides 9187 by NAT_4:9;
    9187 = 67*137 + 8; hence not 67 divides 9187 by NAT_4:9;
    9187 = 71*129 + 28; hence not 71 divides 9187 by NAT_4:9;
    9187 = 73*125 + 62; hence not 73 divides 9187 by NAT_4:9;
    9187 = 79*116 + 23; hence not 79 divides 9187 by NAT_4:9;
    9187 = 83*110 + 57; hence not 83 divides 9187 by NAT_4:9;
    9187 = 89*103 + 20; hence not 89 divides 9187 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9187 & n is prime
  holds not n divides 9187 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
