
theorem
  7789 is prime
proof
  now
    7789 = 2*3894 + 1; hence not 2 divides 7789 by NAT_4:9;
    7789 = 3*2596 + 1; hence not 3 divides 7789 by NAT_4:9;
    7789 = 5*1557 + 4; hence not 5 divides 7789 by NAT_4:9;
    7789 = 7*1112 + 5; hence not 7 divides 7789 by NAT_4:9;
    7789 = 11*708 + 1; hence not 11 divides 7789 by NAT_4:9;
    7789 = 13*599 + 2; hence not 13 divides 7789 by NAT_4:9;
    7789 = 17*458 + 3; hence not 17 divides 7789 by NAT_4:9;
    7789 = 19*409 + 18; hence not 19 divides 7789 by NAT_4:9;
    7789 = 23*338 + 15; hence not 23 divides 7789 by NAT_4:9;
    7789 = 29*268 + 17; hence not 29 divides 7789 by NAT_4:9;
    7789 = 31*251 + 8; hence not 31 divides 7789 by NAT_4:9;
    7789 = 37*210 + 19; hence not 37 divides 7789 by NAT_4:9;
    7789 = 41*189 + 40; hence not 41 divides 7789 by NAT_4:9;
    7789 = 43*181 + 6; hence not 43 divides 7789 by NAT_4:9;
    7789 = 47*165 + 34; hence not 47 divides 7789 by NAT_4:9;
    7789 = 53*146 + 51; hence not 53 divides 7789 by NAT_4:9;
    7789 = 59*132 + 1; hence not 59 divides 7789 by NAT_4:9;
    7789 = 61*127 + 42; hence not 61 divides 7789 by NAT_4:9;
    7789 = 67*116 + 17; hence not 67 divides 7789 by NAT_4:9;
    7789 = 71*109 + 50; hence not 71 divides 7789 by NAT_4:9;
    7789 = 73*106 + 51; hence not 73 divides 7789 by NAT_4:9;
    7789 = 79*98 + 47; hence not 79 divides 7789 by NAT_4:9;
    7789 = 83*93 + 70; hence not 83 divides 7789 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7789 & n is prime
  holds not n divides 7789 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
