
theorem
  5693 is prime
proof
  now
    5693 = 2*2846 + 1; hence not 2 divides 5693 by NAT_4:9;
    5693 = 3*1897 + 2; hence not 3 divides 5693 by NAT_4:9;
    5693 = 5*1138 + 3; hence not 5 divides 5693 by NAT_4:9;
    5693 = 7*813 + 2; hence not 7 divides 5693 by NAT_4:9;
    5693 = 11*517 + 6; hence not 11 divides 5693 by NAT_4:9;
    5693 = 13*437 + 12; hence not 13 divides 5693 by NAT_4:9;
    5693 = 17*334 + 15; hence not 17 divides 5693 by NAT_4:9;
    5693 = 19*299 + 12; hence not 19 divides 5693 by NAT_4:9;
    5693 = 23*247 + 12; hence not 23 divides 5693 by NAT_4:9;
    5693 = 29*196 + 9; hence not 29 divides 5693 by NAT_4:9;
    5693 = 31*183 + 20; hence not 31 divides 5693 by NAT_4:9;
    5693 = 37*153 + 32; hence not 37 divides 5693 by NAT_4:9;
    5693 = 41*138 + 35; hence not 41 divides 5693 by NAT_4:9;
    5693 = 43*132 + 17; hence not 43 divides 5693 by NAT_4:9;
    5693 = 47*121 + 6; hence not 47 divides 5693 by NAT_4:9;
    5693 = 53*107 + 22; hence not 53 divides 5693 by NAT_4:9;
    5693 = 59*96 + 29; hence not 59 divides 5693 by NAT_4:9;
    5693 = 61*93 + 20; hence not 61 divides 5693 by NAT_4:9;
    5693 = 67*84 + 65; hence not 67 divides 5693 by NAT_4:9;
    5693 = 71*80 + 13; hence not 71 divides 5693 by NAT_4:9;
    5693 = 73*77 + 72; hence not 73 divides 5693 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5693 & n is prime
  holds not n divides 5693 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
