
theorem
  8783 is prime
proof
  now
    8783 = 2*4391 + 1; hence not 2 divides 8783 by NAT_4:9;
    8783 = 3*2927 + 2; hence not 3 divides 8783 by NAT_4:9;
    8783 = 5*1756 + 3; hence not 5 divides 8783 by NAT_4:9;
    8783 = 7*1254 + 5; hence not 7 divides 8783 by NAT_4:9;
    8783 = 11*798 + 5; hence not 11 divides 8783 by NAT_4:9;
    8783 = 13*675 + 8; hence not 13 divides 8783 by NAT_4:9;
    8783 = 17*516 + 11; hence not 17 divides 8783 by NAT_4:9;
    8783 = 19*462 + 5; hence not 19 divides 8783 by NAT_4:9;
    8783 = 23*381 + 20; hence not 23 divides 8783 by NAT_4:9;
    8783 = 29*302 + 25; hence not 29 divides 8783 by NAT_4:9;
    8783 = 31*283 + 10; hence not 31 divides 8783 by NAT_4:9;
    8783 = 37*237 + 14; hence not 37 divides 8783 by NAT_4:9;
    8783 = 41*214 + 9; hence not 41 divides 8783 by NAT_4:9;
    8783 = 43*204 + 11; hence not 43 divides 8783 by NAT_4:9;
    8783 = 47*186 + 41; hence not 47 divides 8783 by NAT_4:9;
    8783 = 53*165 + 38; hence not 53 divides 8783 by NAT_4:9;
    8783 = 59*148 + 51; hence not 59 divides 8783 by NAT_4:9;
    8783 = 61*143 + 60; hence not 61 divides 8783 by NAT_4:9;
    8783 = 67*131 + 6; hence not 67 divides 8783 by NAT_4:9;
    8783 = 71*123 + 50; hence not 71 divides 8783 by NAT_4:9;
    8783 = 73*120 + 23; hence not 73 divides 8783 by NAT_4:9;
    8783 = 79*111 + 14; hence not 79 divides 8783 by NAT_4:9;
    8783 = 83*105 + 68; hence not 83 divides 8783 by NAT_4:9;
    8783 = 89*98 + 61; hence not 89 divides 8783 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 8783 & n is prime
  holds not n divides 8783 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
