
theorem
  5939 is prime
proof
  now
    5939 = 2*2969 + 1; hence not 2 divides 5939 by NAT_4:9;
    5939 = 3*1979 + 2; hence not 3 divides 5939 by NAT_4:9;
    5939 = 5*1187 + 4; hence not 5 divides 5939 by NAT_4:9;
    5939 = 7*848 + 3; hence not 7 divides 5939 by NAT_4:9;
    5939 = 11*539 + 10; hence not 11 divides 5939 by NAT_4:9;
    5939 = 13*456 + 11; hence not 13 divides 5939 by NAT_4:9;
    5939 = 17*349 + 6; hence not 17 divides 5939 by NAT_4:9;
    5939 = 19*312 + 11; hence not 19 divides 5939 by NAT_4:9;
    5939 = 23*258 + 5; hence not 23 divides 5939 by NAT_4:9;
    5939 = 29*204 + 23; hence not 29 divides 5939 by NAT_4:9;
    5939 = 31*191 + 18; hence not 31 divides 5939 by NAT_4:9;
    5939 = 37*160 + 19; hence not 37 divides 5939 by NAT_4:9;
    5939 = 41*144 + 35; hence not 41 divides 5939 by NAT_4:9;
    5939 = 43*138 + 5; hence not 43 divides 5939 by NAT_4:9;
    5939 = 47*126 + 17; hence not 47 divides 5939 by NAT_4:9;
    5939 = 53*112 + 3; hence not 53 divides 5939 by NAT_4:9;
    5939 = 59*100 + 39; hence not 59 divides 5939 by NAT_4:9;
    5939 = 61*97 + 22; hence not 61 divides 5939 by NAT_4:9;
    5939 = 67*88 + 43; hence not 67 divides 5939 by NAT_4:9;
    5939 = 71*83 + 46; hence not 71 divides 5939 by NAT_4:9;
    5939 = 73*81 + 26; hence not 73 divides 5939 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5939 & n is prime
  holds not n divides 5939 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
