
theorem
  7691 is prime
proof
  now
    7691 = 2*3845 + 1; hence not 2 divides 7691 by NAT_4:9;
    7691 = 3*2563 + 2; hence not 3 divides 7691 by NAT_4:9;
    7691 = 5*1538 + 1; hence not 5 divides 7691 by NAT_4:9;
    7691 = 7*1098 + 5; hence not 7 divides 7691 by NAT_4:9;
    7691 = 11*699 + 2; hence not 11 divides 7691 by NAT_4:9;
    7691 = 13*591 + 8; hence not 13 divides 7691 by NAT_4:9;
    7691 = 17*452 + 7; hence not 17 divides 7691 by NAT_4:9;
    7691 = 19*404 + 15; hence not 19 divides 7691 by NAT_4:9;
    7691 = 23*334 + 9; hence not 23 divides 7691 by NAT_4:9;
    7691 = 29*265 + 6; hence not 29 divides 7691 by NAT_4:9;
    7691 = 31*248 + 3; hence not 31 divides 7691 by NAT_4:9;
    7691 = 37*207 + 32; hence not 37 divides 7691 by NAT_4:9;
    7691 = 41*187 + 24; hence not 41 divides 7691 by NAT_4:9;
    7691 = 43*178 + 37; hence not 43 divides 7691 by NAT_4:9;
    7691 = 47*163 + 30; hence not 47 divides 7691 by NAT_4:9;
    7691 = 53*145 + 6; hence not 53 divides 7691 by NAT_4:9;
    7691 = 59*130 + 21; hence not 59 divides 7691 by NAT_4:9;
    7691 = 61*126 + 5; hence not 61 divides 7691 by NAT_4:9;
    7691 = 67*114 + 53; hence not 67 divides 7691 by NAT_4:9;
    7691 = 71*108 + 23; hence not 71 divides 7691 by NAT_4:9;
    7691 = 73*105 + 26; hence not 73 divides 7691 by NAT_4:9;
    7691 = 79*97 + 28; hence not 79 divides 7691 by NAT_4:9;
    7691 = 83*92 + 55; hence not 83 divides 7691 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7691 & n is prime
  holds not n divides 7691 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
