
theorem
  7699 is prime
proof
  now
    7699 = 2*3849 + 1; hence not 2 divides 7699 by NAT_4:9;
    7699 = 3*2566 + 1; hence not 3 divides 7699 by NAT_4:9;
    7699 = 5*1539 + 4; hence not 5 divides 7699 by NAT_4:9;
    7699 = 7*1099 + 6; hence not 7 divides 7699 by NAT_4:9;
    7699 = 11*699 + 10; hence not 11 divides 7699 by NAT_4:9;
    7699 = 13*592 + 3; hence not 13 divides 7699 by NAT_4:9;
    7699 = 17*452 + 15; hence not 17 divides 7699 by NAT_4:9;
    7699 = 19*405 + 4; hence not 19 divides 7699 by NAT_4:9;
    7699 = 23*334 + 17; hence not 23 divides 7699 by NAT_4:9;
    7699 = 29*265 + 14; hence not 29 divides 7699 by NAT_4:9;
    7699 = 31*248 + 11; hence not 31 divides 7699 by NAT_4:9;
    7699 = 37*208 + 3; hence not 37 divides 7699 by NAT_4:9;
    7699 = 41*187 + 32; hence not 41 divides 7699 by NAT_4:9;
    7699 = 43*179 + 2; hence not 43 divides 7699 by NAT_4:9;
    7699 = 47*163 + 38; hence not 47 divides 7699 by NAT_4:9;
    7699 = 53*145 + 14; hence not 53 divides 7699 by NAT_4:9;
    7699 = 59*130 + 29; hence not 59 divides 7699 by NAT_4:9;
    7699 = 61*126 + 13; hence not 61 divides 7699 by NAT_4:9;
    7699 = 67*114 + 61; hence not 67 divides 7699 by NAT_4:9;
    7699 = 71*108 + 31; hence not 71 divides 7699 by NAT_4:9;
    7699 = 73*105 + 34; hence not 73 divides 7699 by NAT_4:9;
    7699 = 79*97 + 36; hence not 79 divides 7699 by NAT_4:9;
    7699 = 83*92 + 63; hence not 83 divides 7699 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7699 & n is prime
  holds not n divides 7699 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
