
theorem
  5743 is prime
proof
  now
    5743 = 2*2871 + 1; hence not 2 divides 5743 by NAT_4:9;
    5743 = 3*1914 + 1; hence not 3 divides 5743 by NAT_4:9;
    5743 = 5*1148 + 3; hence not 5 divides 5743 by NAT_4:9;
    5743 = 7*820 + 3; hence not 7 divides 5743 by NAT_4:9;
    5743 = 11*522 + 1; hence not 11 divides 5743 by NAT_4:9;
    5743 = 13*441 + 10; hence not 13 divides 5743 by NAT_4:9;
    5743 = 17*337 + 14; hence not 17 divides 5743 by NAT_4:9;
    5743 = 19*302 + 5; hence not 19 divides 5743 by NAT_4:9;
    5743 = 23*249 + 16; hence not 23 divides 5743 by NAT_4:9;
    5743 = 29*198 + 1; hence not 29 divides 5743 by NAT_4:9;
    5743 = 31*185 + 8; hence not 31 divides 5743 by NAT_4:9;
    5743 = 37*155 + 8; hence not 37 divides 5743 by NAT_4:9;
    5743 = 41*140 + 3; hence not 41 divides 5743 by NAT_4:9;
    5743 = 43*133 + 24; hence not 43 divides 5743 by NAT_4:9;
    5743 = 47*122 + 9; hence not 47 divides 5743 by NAT_4:9;
    5743 = 53*108 + 19; hence not 53 divides 5743 by NAT_4:9;
    5743 = 59*97 + 20; hence not 59 divides 5743 by NAT_4:9;
    5743 = 61*94 + 9; hence not 61 divides 5743 by NAT_4:9;
    5743 = 67*85 + 48; hence not 67 divides 5743 by NAT_4:9;
    5743 = 71*80 + 63; hence not 71 divides 5743 by NAT_4:9;
    5743 = 73*78 + 49; hence not 73 divides 5743 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5743 & n is prime
  holds not n divides 5743 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
