
theorem
  7993 is prime
proof
  now
    7993 = 2*3996 + 1; hence not 2 divides 7993 by NAT_4:9;
    7993 = 3*2664 + 1; hence not 3 divides 7993 by NAT_4:9;
    7993 = 5*1598 + 3; hence not 5 divides 7993 by NAT_4:9;
    7993 = 7*1141 + 6; hence not 7 divides 7993 by NAT_4:9;
    7993 = 11*726 + 7; hence not 11 divides 7993 by NAT_4:9;
    7993 = 13*614 + 11; hence not 13 divides 7993 by NAT_4:9;
    7993 = 17*470 + 3; hence not 17 divides 7993 by NAT_4:9;
    7993 = 19*420 + 13; hence not 19 divides 7993 by NAT_4:9;
    7993 = 23*347 + 12; hence not 23 divides 7993 by NAT_4:9;
    7993 = 29*275 + 18; hence not 29 divides 7993 by NAT_4:9;
    7993 = 31*257 + 26; hence not 31 divides 7993 by NAT_4:9;
    7993 = 37*216 + 1; hence not 37 divides 7993 by NAT_4:9;
    7993 = 41*194 + 39; hence not 41 divides 7993 by NAT_4:9;
    7993 = 43*185 + 38; hence not 43 divides 7993 by NAT_4:9;
    7993 = 47*170 + 3; hence not 47 divides 7993 by NAT_4:9;
    7993 = 53*150 + 43; hence not 53 divides 7993 by NAT_4:9;
    7993 = 59*135 + 28; hence not 59 divides 7993 by NAT_4:9;
    7993 = 61*131 + 2; hence not 61 divides 7993 by NAT_4:9;
    7993 = 67*119 + 20; hence not 67 divides 7993 by NAT_4:9;
    7993 = 71*112 + 41; hence not 71 divides 7993 by NAT_4:9;
    7993 = 73*109 + 36; hence not 73 divides 7993 by NAT_4:9;
    7993 = 79*101 + 14; hence not 79 divides 7993 by NAT_4:9;
    7993 = 83*96 + 25; hence not 83 divides 7993 by NAT_4:9;
    7993 = 89*89 + 72; hence not 89 divides 7993 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7993 & n is prime
  holds not n divides 7993 by XPRIMET1:48;
  hence thesis by NAT_4:14;
end;
