
theorem
  5923 is prime
proof
  now
    5923 = 2*2961 + 1; hence not 2 divides 5923 by NAT_4:9;
    5923 = 3*1974 + 1; hence not 3 divides 5923 by NAT_4:9;
    5923 = 5*1184 + 3; hence not 5 divides 5923 by NAT_4:9;
    5923 = 7*846 + 1; hence not 7 divides 5923 by NAT_4:9;
    5923 = 11*538 + 5; hence not 11 divides 5923 by NAT_4:9;
    5923 = 13*455 + 8; hence not 13 divides 5923 by NAT_4:9;
    5923 = 17*348 + 7; hence not 17 divides 5923 by NAT_4:9;
    5923 = 19*311 + 14; hence not 19 divides 5923 by NAT_4:9;
    5923 = 23*257 + 12; hence not 23 divides 5923 by NAT_4:9;
    5923 = 29*204 + 7; hence not 29 divides 5923 by NAT_4:9;
    5923 = 31*191 + 2; hence not 31 divides 5923 by NAT_4:9;
    5923 = 37*160 + 3; hence not 37 divides 5923 by NAT_4:9;
    5923 = 41*144 + 19; hence not 41 divides 5923 by NAT_4:9;
    5923 = 43*137 + 32; hence not 43 divides 5923 by NAT_4:9;
    5923 = 47*126 + 1; hence not 47 divides 5923 by NAT_4:9;
    5923 = 53*111 + 40; hence not 53 divides 5923 by NAT_4:9;
    5923 = 59*100 + 23; hence not 59 divides 5923 by NAT_4:9;
    5923 = 61*97 + 6; hence not 61 divides 5923 by NAT_4:9;
    5923 = 67*88 + 27; hence not 67 divides 5923 by NAT_4:9;
    5923 = 71*83 + 30; hence not 71 divides 5923 by NAT_4:9;
    5923 = 73*81 + 10; hence not 73 divides 5923 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5923 & n is prime
  holds not n divides 5923 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
