
theorem
  5701 is prime
proof
  now
    5701 = 2*2850 + 1; hence not 2 divides 5701 by NAT_4:9;
    5701 = 3*1900 + 1; hence not 3 divides 5701 by NAT_4:9;
    5701 = 5*1140 + 1; hence not 5 divides 5701 by NAT_4:9;
    5701 = 7*814 + 3; hence not 7 divides 5701 by NAT_4:9;
    5701 = 11*518 + 3; hence not 11 divides 5701 by NAT_4:9;
    5701 = 13*438 + 7; hence not 13 divides 5701 by NAT_4:9;
    5701 = 17*335 + 6; hence not 17 divides 5701 by NAT_4:9;
    5701 = 19*300 + 1; hence not 19 divides 5701 by NAT_4:9;
    5701 = 23*247 + 20; hence not 23 divides 5701 by NAT_4:9;
    5701 = 29*196 + 17; hence not 29 divides 5701 by NAT_4:9;
    5701 = 31*183 + 28; hence not 31 divides 5701 by NAT_4:9;
    5701 = 37*154 + 3; hence not 37 divides 5701 by NAT_4:9;
    5701 = 41*139 + 2; hence not 41 divides 5701 by NAT_4:9;
    5701 = 43*132 + 25; hence not 43 divides 5701 by NAT_4:9;
    5701 = 47*121 + 14; hence not 47 divides 5701 by NAT_4:9;
    5701 = 53*107 + 30; hence not 53 divides 5701 by NAT_4:9;
    5701 = 59*96 + 37; hence not 59 divides 5701 by NAT_4:9;
    5701 = 61*93 + 28; hence not 61 divides 5701 by NAT_4:9;
    5701 = 67*85 + 6; hence not 67 divides 5701 by NAT_4:9;
    5701 = 71*80 + 21; hence not 71 divides 5701 by NAT_4:9;
    5701 = 73*78 + 7; hence not 73 divides 5701 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5701 & n is prime
  holds not n divides 5701 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
