
theorem
  7687 is prime
proof
  now
    7687 = 2*3843 + 1; hence not 2 divides 7687 by NAT_4:9;
    7687 = 3*2562 + 1; hence not 3 divides 7687 by NAT_4:9;
    7687 = 5*1537 + 2; hence not 5 divides 7687 by NAT_4:9;
    7687 = 7*1098 + 1; hence not 7 divides 7687 by NAT_4:9;
    7687 = 11*698 + 9; hence not 11 divides 7687 by NAT_4:9;
    7687 = 13*591 + 4; hence not 13 divides 7687 by NAT_4:9;
    7687 = 17*452 + 3; hence not 17 divides 7687 by NAT_4:9;
    7687 = 19*404 + 11; hence not 19 divides 7687 by NAT_4:9;
    7687 = 23*334 + 5; hence not 23 divides 7687 by NAT_4:9;
    7687 = 29*265 + 2; hence not 29 divides 7687 by NAT_4:9;
    7687 = 31*247 + 30; hence not 31 divides 7687 by NAT_4:9;
    7687 = 37*207 + 28; hence not 37 divides 7687 by NAT_4:9;
    7687 = 41*187 + 20; hence not 41 divides 7687 by NAT_4:9;
    7687 = 43*178 + 33; hence not 43 divides 7687 by NAT_4:9;
    7687 = 47*163 + 26; hence not 47 divides 7687 by NAT_4:9;
    7687 = 53*145 + 2; hence not 53 divides 7687 by NAT_4:9;
    7687 = 59*130 + 17; hence not 59 divides 7687 by NAT_4:9;
    7687 = 61*126 + 1; hence not 61 divides 7687 by NAT_4:9;
    7687 = 67*114 + 49; hence not 67 divides 7687 by NAT_4:9;
    7687 = 71*108 + 19; hence not 71 divides 7687 by NAT_4:9;
    7687 = 73*105 + 22; hence not 73 divides 7687 by NAT_4:9;
    7687 = 79*97 + 24; hence not 79 divides 7687 by NAT_4:9;
    7687 = 83*92 + 51; hence not 83 divides 7687 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7687 & n is prime
  holds not n divides 7687 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
