
theorem
  7681 is prime
proof
  now
    7681 = 2*3840 + 1; hence not 2 divides 7681 by NAT_4:9;
    7681 = 3*2560 + 1; hence not 3 divides 7681 by NAT_4:9;
    7681 = 5*1536 + 1; hence not 5 divides 7681 by NAT_4:9;
    7681 = 7*1097 + 2; hence not 7 divides 7681 by NAT_4:9;
    7681 = 11*698 + 3; hence not 11 divides 7681 by NAT_4:9;
    7681 = 13*590 + 11; hence not 13 divides 7681 by NAT_4:9;
    7681 = 17*451 + 14; hence not 17 divides 7681 by NAT_4:9;
    7681 = 19*404 + 5; hence not 19 divides 7681 by NAT_4:9;
    7681 = 23*333 + 22; hence not 23 divides 7681 by NAT_4:9;
    7681 = 29*264 + 25; hence not 29 divides 7681 by NAT_4:9;
    7681 = 31*247 + 24; hence not 31 divides 7681 by NAT_4:9;
    7681 = 37*207 + 22; hence not 37 divides 7681 by NAT_4:9;
    7681 = 41*187 + 14; hence not 41 divides 7681 by NAT_4:9;
    7681 = 43*178 + 27; hence not 43 divides 7681 by NAT_4:9;
    7681 = 47*163 + 20; hence not 47 divides 7681 by NAT_4:9;
    7681 = 53*144 + 49; hence not 53 divides 7681 by NAT_4:9;
    7681 = 59*130 + 11; hence not 59 divides 7681 by NAT_4:9;
    7681 = 61*125 + 56; hence not 61 divides 7681 by NAT_4:9;
    7681 = 67*114 + 43; hence not 67 divides 7681 by NAT_4:9;
    7681 = 71*108 + 13; hence not 71 divides 7681 by NAT_4:9;
    7681 = 73*105 + 16; hence not 73 divides 7681 by NAT_4:9;
    7681 = 79*97 + 18; hence not 79 divides 7681 by NAT_4:9;
    7681 = 83*92 + 45; hence not 83 divides 7681 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7681 & n is prime
  holds not n divides 7681 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
