
theorem
  9137 is prime
proof
  now
    9137 = 2*4568 + 1; hence not 2 divides 9137 by NAT_4:9;
    9137 = 3*3045 + 2; hence not 3 divides 9137 by NAT_4:9;
    9137 = 5*1827 + 2; hence not 5 divides 9137 by NAT_4:9;
    9137 = 7*1305 + 2; hence not 7 divides 9137 by NAT_4:9;
    9137 = 11*830 + 7; hence not 11 divides 9137 by NAT_4:9;
    9137 = 13*702 + 11; hence not 13 divides 9137 by NAT_4:9;
    9137 = 17*537 + 8; hence not 17 divides 9137 by NAT_4:9;
    9137 = 19*480 + 17; hence not 19 divides 9137 by NAT_4:9;
    9137 = 23*397 + 6; hence not 23 divides 9137 by NAT_4:9;
    9137 = 29*315 + 2; hence not 29 divides 9137 by NAT_4:9;
    9137 = 31*294 + 23; hence not 31 divides 9137 by NAT_4:9;
    9137 = 37*246 + 35; hence not 37 divides 9137 by NAT_4:9;
    9137 = 41*222 + 35; hence not 41 divides 9137 by NAT_4:9;
    9137 = 43*212 + 21; hence not 43 divides 9137 by NAT_4:9;
    9137 = 47*194 + 19; hence not 47 divides 9137 by NAT_4:9;
    9137 = 53*172 + 21; hence not 53 divides 9137 by NAT_4:9;
    9137 = 59*154 + 51; hence not 59 divides 9137 by NAT_4:9;
    9137 = 61*149 + 48; hence not 61 divides 9137 by NAT_4:9;
    9137 = 67*136 + 25; hence not 67 divides 9137 by NAT_4:9;
    9137 = 71*128 + 49; hence not 71 divides 9137 by NAT_4:9;
    9137 = 73*125 + 12; hence not 73 divides 9137 by NAT_4:9;
    9137 = 79*115 + 52; hence not 79 divides 9137 by NAT_4:9;
    9137 = 83*110 + 7; hence not 83 divides 9137 by NAT_4:9;
    9137 = 89*102 + 59; hence not 89 divides 9137 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9137 & n is prime
  holds not n divides 9137 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
