
theorem
  9059 is prime
proof
  now
    9059 = 2*4529 + 1; hence not 2 divides 9059 by NAT_4:9;
    9059 = 3*3019 + 2; hence not 3 divides 9059 by NAT_4:9;
    9059 = 5*1811 + 4; hence not 5 divides 9059 by NAT_4:9;
    9059 = 7*1294 + 1; hence not 7 divides 9059 by NAT_4:9;
    9059 = 11*823 + 6; hence not 11 divides 9059 by NAT_4:9;
    9059 = 13*696 + 11; hence not 13 divides 9059 by NAT_4:9;
    9059 = 17*532 + 15; hence not 17 divides 9059 by NAT_4:9;
    9059 = 19*476 + 15; hence not 19 divides 9059 by NAT_4:9;
    9059 = 23*393 + 20; hence not 23 divides 9059 by NAT_4:9;
    9059 = 29*312 + 11; hence not 29 divides 9059 by NAT_4:9;
    9059 = 31*292 + 7; hence not 31 divides 9059 by NAT_4:9;
    9059 = 37*244 + 31; hence not 37 divides 9059 by NAT_4:9;
    9059 = 41*220 + 39; hence not 41 divides 9059 by NAT_4:9;
    9059 = 43*210 + 29; hence not 43 divides 9059 by NAT_4:9;
    9059 = 47*192 + 35; hence not 47 divides 9059 by NAT_4:9;
    9059 = 53*170 + 49; hence not 53 divides 9059 by NAT_4:9;
    9059 = 59*153 + 32; hence not 59 divides 9059 by NAT_4:9;
    9059 = 61*148 + 31; hence not 61 divides 9059 by NAT_4:9;
    9059 = 67*135 + 14; hence not 67 divides 9059 by NAT_4:9;
    9059 = 71*127 + 42; hence not 71 divides 9059 by NAT_4:9;
    9059 = 73*124 + 7; hence not 73 divides 9059 by NAT_4:9;
    9059 = 79*114 + 53; hence not 79 divides 9059 by NAT_4:9;
    9059 = 83*109 + 12; hence not 83 divides 9059 by NAT_4:9;
    9059 = 89*101 + 70; hence not 89 divides 9059 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9059 & n is prime
  holds not n divides 9059 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
