
theorem
  7817 is prime
proof
  now
    7817 = 2*3908 + 1; hence not 2 divides 7817 by NAT_4:9;
    7817 = 3*2605 + 2; hence not 3 divides 7817 by NAT_4:9;
    7817 = 5*1563 + 2; hence not 5 divides 7817 by NAT_4:9;
    7817 = 7*1116 + 5; hence not 7 divides 7817 by NAT_4:9;
    7817 = 11*710 + 7; hence not 11 divides 7817 by NAT_4:9;
    7817 = 13*601 + 4; hence not 13 divides 7817 by NAT_4:9;
    7817 = 17*459 + 14; hence not 17 divides 7817 by NAT_4:9;
    7817 = 19*411 + 8; hence not 19 divides 7817 by NAT_4:9;
    7817 = 23*339 + 20; hence not 23 divides 7817 by NAT_4:9;
    7817 = 29*269 + 16; hence not 29 divides 7817 by NAT_4:9;
    7817 = 31*252 + 5; hence not 31 divides 7817 by NAT_4:9;
    7817 = 37*211 + 10; hence not 37 divides 7817 by NAT_4:9;
    7817 = 41*190 + 27; hence not 41 divides 7817 by NAT_4:9;
    7817 = 43*181 + 34; hence not 43 divides 7817 by NAT_4:9;
    7817 = 47*166 + 15; hence not 47 divides 7817 by NAT_4:9;
    7817 = 53*147 + 26; hence not 53 divides 7817 by NAT_4:9;
    7817 = 59*132 + 29; hence not 59 divides 7817 by NAT_4:9;
    7817 = 61*128 + 9; hence not 61 divides 7817 by NAT_4:9;
    7817 = 67*116 + 45; hence not 67 divides 7817 by NAT_4:9;
    7817 = 71*110 + 7; hence not 71 divides 7817 by NAT_4:9;
    7817 = 73*107 + 6; hence not 73 divides 7817 by NAT_4:9;
    7817 = 79*98 + 75; hence not 79 divides 7817 by NAT_4:9;
    7817 = 83*94 + 15; hence not 83 divides 7817 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7817 & n is prime
  holds not n divides 7817 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
