
theorem
  7793 is prime
proof
  now
    7793 = 2*3896 + 1; hence not 2 divides 7793 by NAT_4:9;
    7793 = 3*2597 + 2; hence not 3 divides 7793 by NAT_4:9;
    7793 = 5*1558 + 3; hence not 5 divides 7793 by NAT_4:9;
    7793 = 7*1113 + 2; hence not 7 divides 7793 by NAT_4:9;
    7793 = 11*708 + 5; hence not 11 divides 7793 by NAT_4:9;
    7793 = 13*599 + 6; hence not 13 divides 7793 by NAT_4:9;
    7793 = 17*458 + 7; hence not 17 divides 7793 by NAT_4:9;
    7793 = 19*410 + 3; hence not 19 divides 7793 by NAT_4:9;
    7793 = 23*338 + 19; hence not 23 divides 7793 by NAT_4:9;
    7793 = 29*268 + 21; hence not 29 divides 7793 by NAT_4:9;
    7793 = 31*251 + 12; hence not 31 divides 7793 by NAT_4:9;
    7793 = 37*210 + 23; hence not 37 divides 7793 by NAT_4:9;
    7793 = 41*190 + 3; hence not 41 divides 7793 by NAT_4:9;
    7793 = 43*181 + 10; hence not 43 divides 7793 by NAT_4:9;
    7793 = 47*165 + 38; hence not 47 divides 7793 by NAT_4:9;
    7793 = 53*147 + 2; hence not 53 divides 7793 by NAT_4:9;
    7793 = 59*132 + 5; hence not 59 divides 7793 by NAT_4:9;
    7793 = 61*127 + 46; hence not 61 divides 7793 by NAT_4:9;
    7793 = 67*116 + 21; hence not 67 divides 7793 by NAT_4:9;
    7793 = 71*109 + 54; hence not 71 divides 7793 by NAT_4:9;
    7793 = 73*106 + 55; hence not 73 divides 7793 by NAT_4:9;
    7793 = 79*98 + 51; hence not 79 divides 7793 by NAT_4:9;
    7793 = 83*93 + 74; hence not 83 divides 7793 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7793 & n is prime
  holds not n divides 7793 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
