
theorem
  7717 is prime
proof
  now
    7717 = 2*3858 + 1; hence not 2 divides 7717 by NAT_4:9;
    7717 = 3*2572 + 1; hence not 3 divides 7717 by NAT_4:9;
    7717 = 5*1543 + 2; hence not 5 divides 7717 by NAT_4:9;
    7717 = 7*1102 + 3; hence not 7 divides 7717 by NAT_4:9;
    7717 = 11*701 + 6; hence not 11 divides 7717 by NAT_4:9;
    7717 = 13*593 + 8; hence not 13 divides 7717 by NAT_4:9;
    7717 = 17*453 + 16; hence not 17 divides 7717 by NAT_4:9;
    7717 = 19*406 + 3; hence not 19 divides 7717 by NAT_4:9;
    7717 = 23*335 + 12; hence not 23 divides 7717 by NAT_4:9;
    7717 = 29*266 + 3; hence not 29 divides 7717 by NAT_4:9;
    7717 = 31*248 + 29; hence not 31 divides 7717 by NAT_4:9;
    7717 = 37*208 + 21; hence not 37 divides 7717 by NAT_4:9;
    7717 = 41*188 + 9; hence not 41 divides 7717 by NAT_4:9;
    7717 = 43*179 + 20; hence not 43 divides 7717 by NAT_4:9;
    7717 = 47*164 + 9; hence not 47 divides 7717 by NAT_4:9;
    7717 = 53*145 + 32; hence not 53 divides 7717 by NAT_4:9;
    7717 = 59*130 + 47; hence not 59 divides 7717 by NAT_4:9;
    7717 = 61*126 + 31; hence not 61 divides 7717 by NAT_4:9;
    7717 = 67*115 + 12; hence not 67 divides 7717 by NAT_4:9;
    7717 = 71*108 + 49; hence not 71 divides 7717 by NAT_4:9;
    7717 = 73*105 + 52; hence not 73 divides 7717 by NAT_4:9;
    7717 = 79*97 + 54; hence not 79 divides 7717 by NAT_4:9;
    7717 = 83*92 + 81; hence not 83 divides 7717 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7717 & n is prime
  holds not n divides 7717 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
