
theorem
  9041 is prime
proof
  now
    9041 = 2*4520 + 1; hence not 2 divides 9041 by NAT_4:9;
    9041 = 3*3013 + 2; hence not 3 divides 9041 by NAT_4:9;
    9041 = 5*1808 + 1; hence not 5 divides 9041 by NAT_4:9;
    9041 = 7*1291 + 4; hence not 7 divides 9041 by NAT_4:9;
    9041 = 11*821 + 10; hence not 11 divides 9041 by NAT_4:9;
    9041 = 13*695 + 6; hence not 13 divides 9041 by NAT_4:9;
    9041 = 17*531 + 14; hence not 17 divides 9041 by NAT_4:9;
    9041 = 19*475 + 16; hence not 19 divides 9041 by NAT_4:9;
    9041 = 23*393 + 2; hence not 23 divides 9041 by NAT_4:9;
    9041 = 29*311 + 22; hence not 29 divides 9041 by NAT_4:9;
    9041 = 31*291 + 20; hence not 31 divides 9041 by NAT_4:9;
    9041 = 37*244 + 13; hence not 37 divides 9041 by NAT_4:9;
    9041 = 41*220 + 21; hence not 41 divides 9041 by NAT_4:9;
    9041 = 43*210 + 11; hence not 43 divides 9041 by NAT_4:9;
    9041 = 47*192 + 17; hence not 47 divides 9041 by NAT_4:9;
    9041 = 53*170 + 31; hence not 53 divides 9041 by NAT_4:9;
    9041 = 59*153 + 14; hence not 59 divides 9041 by NAT_4:9;
    9041 = 61*148 + 13; hence not 61 divides 9041 by NAT_4:9;
    9041 = 67*134 + 63; hence not 67 divides 9041 by NAT_4:9;
    9041 = 71*127 + 24; hence not 71 divides 9041 by NAT_4:9;
    9041 = 73*123 + 62; hence not 73 divides 9041 by NAT_4:9;
    9041 = 79*114 + 35; hence not 79 divides 9041 by NAT_4:9;
    9041 = 83*108 + 77; hence not 83 divides 9041 by NAT_4:9;
    9041 = 89*101 + 52; hence not 89 divides 9041 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9041 & n is prime
  holds not n divides 9041 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
