
theorem
  7823 is prime
proof
  now
    7823 = 2*3911 + 1; hence not 2 divides 7823 by NAT_4:9;
    7823 = 3*2607 + 2; hence not 3 divides 7823 by NAT_4:9;
    7823 = 5*1564 + 3; hence not 5 divides 7823 by NAT_4:9;
    7823 = 7*1117 + 4; hence not 7 divides 7823 by NAT_4:9;
    7823 = 11*711 + 2; hence not 11 divides 7823 by NAT_4:9;
    7823 = 13*601 + 10; hence not 13 divides 7823 by NAT_4:9;
    7823 = 17*460 + 3; hence not 17 divides 7823 by NAT_4:9;
    7823 = 19*411 + 14; hence not 19 divides 7823 by NAT_4:9;
    7823 = 23*340 + 3; hence not 23 divides 7823 by NAT_4:9;
    7823 = 29*269 + 22; hence not 29 divides 7823 by NAT_4:9;
    7823 = 31*252 + 11; hence not 31 divides 7823 by NAT_4:9;
    7823 = 37*211 + 16; hence not 37 divides 7823 by NAT_4:9;
    7823 = 41*190 + 33; hence not 41 divides 7823 by NAT_4:9;
    7823 = 43*181 + 40; hence not 43 divides 7823 by NAT_4:9;
    7823 = 47*166 + 21; hence not 47 divides 7823 by NAT_4:9;
    7823 = 53*147 + 32; hence not 53 divides 7823 by NAT_4:9;
    7823 = 59*132 + 35; hence not 59 divides 7823 by NAT_4:9;
    7823 = 61*128 + 15; hence not 61 divides 7823 by NAT_4:9;
    7823 = 67*116 + 51; hence not 67 divides 7823 by NAT_4:9;
    7823 = 71*110 + 13; hence not 71 divides 7823 by NAT_4:9;
    7823 = 73*107 + 12; hence not 73 divides 7823 by NAT_4:9;
    7823 = 79*99 + 2; hence not 79 divides 7823 by NAT_4:9;
    7823 = 83*94 + 21; hence not 83 divides 7823 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7823 & n is prime
  holds not n divides 7823 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
