
theorem
  5717 is prime
proof
  now
    5717 = 2*2858 + 1; hence not 2 divides 5717 by NAT_4:9;
    5717 = 3*1905 + 2; hence not 3 divides 5717 by NAT_4:9;
    5717 = 5*1143 + 2; hence not 5 divides 5717 by NAT_4:9;
    5717 = 7*816 + 5; hence not 7 divides 5717 by NAT_4:9;
    5717 = 11*519 + 8; hence not 11 divides 5717 by NAT_4:9;
    5717 = 13*439 + 10; hence not 13 divides 5717 by NAT_4:9;
    5717 = 17*336 + 5; hence not 17 divides 5717 by NAT_4:9;
    5717 = 19*300 + 17; hence not 19 divides 5717 by NAT_4:9;
    5717 = 23*248 + 13; hence not 23 divides 5717 by NAT_4:9;
    5717 = 29*197 + 4; hence not 29 divides 5717 by NAT_4:9;
    5717 = 31*184 + 13; hence not 31 divides 5717 by NAT_4:9;
    5717 = 37*154 + 19; hence not 37 divides 5717 by NAT_4:9;
    5717 = 41*139 + 18; hence not 41 divides 5717 by NAT_4:9;
    5717 = 43*132 + 41; hence not 43 divides 5717 by NAT_4:9;
    5717 = 47*121 + 30; hence not 47 divides 5717 by NAT_4:9;
    5717 = 53*107 + 46; hence not 53 divides 5717 by NAT_4:9;
    5717 = 59*96 + 53; hence not 59 divides 5717 by NAT_4:9;
    5717 = 61*93 + 44; hence not 61 divides 5717 by NAT_4:9;
    5717 = 67*85 + 22; hence not 67 divides 5717 by NAT_4:9;
    5717 = 71*80 + 37; hence not 71 divides 5717 by NAT_4:9;
    5717 = 73*78 + 23; hence not 73 divides 5717 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5717 & n is prime
  holds not n divides 5717 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
