
theorem
  5711 is prime
proof
  now
    5711 = 2*2855 + 1; hence not 2 divides 5711 by NAT_4:9;
    5711 = 3*1903 + 2; hence not 3 divides 5711 by NAT_4:9;
    5711 = 5*1142 + 1; hence not 5 divides 5711 by NAT_4:9;
    5711 = 7*815 + 6; hence not 7 divides 5711 by NAT_4:9;
    5711 = 11*519 + 2; hence not 11 divides 5711 by NAT_4:9;
    5711 = 13*439 + 4; hence not 13 divides 5711 by NAT_4:9;
    5711 = 17*335 + 16; hence not 17 divides 5711 by NAT_4:9;
    5711 = 19*300 + 11; hence not 19 divides 5711 by NAT_4:9;
    5711 = 23*248 + 7; hence not 23 divides 5711 by NAT_4:9;
    5711 = 29*196 + 27; hence not 29 divides 5711 by NAT_4:9;
    5711 = 31*184 + 7; hence not 31 divides 5711 by NAT_4:9;
    5711 = 37*154 + 13; hence not 37 divides 5711 by NAT_4:9;
    5711 = 41*139 + 12; hence not 41 divides 5711 by NAT_4:9;
    5711 = 43*132 + 35; hence not 43 divides 5711 by NAT_4:9;
    5711 = 47*121 + 24; hence not 47 divides 5711 by NAT_4:9;
    5711 = 53*107 + 40; hence not 53 divides 5711 by NAT_4:9;
    5711 = 59*96 + 47; hence not 59 divides 5711 by NAT_4:9;
    5711 = 61*93 + 38; hence not 61 divides 5711 by NAT_4:9;
    5711 = 67*85 + 16; hence not 67 divides 5711 by NAT_4:9;
    5711 = 71*80 + 31; hence not 71 divides 5711 by NAT_4:9;
    5711 = 73*78 + 17; hence not 73 divides 5711 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5711 & n is prime
  holds not n divides 5711 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
