
theorem
  4241 is prime
proof
  now
    4241 = 2*2120 + 1; hence not 2 divides 4241 by NAT_4:9;
    4241 = 3*1413 + 2; hence not 3 divides 4241 by NAT_4:9;
    4241 = 5*848 + 1; hence not 5 divides 4241 by NAT_4:9;
    4241 = 7*605 + 6; hence not 7 divides 4241 by NAT_4:9;
    4241 = 11*385 + 6; hence not 11 divides 4241 by NAT_4:9;
    4241 = 13*326 + 3; hence not 13 divides 4241 by NAT_4:9;
    4241 = 17*249 + 8; hence not 17 divides 4241 by NAT_4:9;
    4241 = 19*223 + 4; hence not 19 divides 4241 by NAT_4:9;
    4241 = 23*184 + 9; hence not 23 divides 4241 by NAT_4:9;
    4241 = 29*146 + 7; hence not 29 divides 4241 by NAT_4:9;
    4241 = 31*136 + 25; hence not 31 divides 4241 by NAT_4:9;
    4241 = 37*114 + 23; hence not 37 divides 4241 by NAT_4:9;
    4241 = 41*103 + 18; hence not 41 divides 4241 by NAT_4:9;
    4241 = 43*98 + 27; hence not 43 divides 4241 by NAT_4:9;
    4241 = 47*90 + 11; hence not 47 divides 4241 by NAT_4:9;
    4241 = 53*80 + 1; hence not 53 divides 4241 by NAT_4:9;
    4241 = 59*71 + 52; hence not 59 divides 4241 by NAT_4:9;
    4241 = 61*69 + 32; hence not 61 divides 4241 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4241 & n is prime
  holds not n divides 4241 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
