
theorem
  5737 is prime
proof
  now
    5737 = 2*2868 + 1; hence not 2 divides 5737 by NAT_4:9;
    5737 = 3*1912 + 1; hence not 3 divides 5737 by NAT_4:9;
    5737 = 5*1147 + 2; hence not 5 divides 5737 by NAT_4:9;
    5737 = 7*819 + 4; hence not 7 divides 5737 by NAT_4:9;
    5737 = 11*521 + 6; hence not 11 divides 5737 by NAT_4:9;
    5737 = 13*441 + 4; hence not 13 divides 5737 by NAT_4:9;
    5737 = 17*337 + 8; hence not 17 divides 5737 by NAT_4:9;
    5737 = 19*301 + 18; hence not 19 divides 5737 by NAT_4:9;
    5737 = 23*249 + 10; hence not 23 divides 5737 by NAT_4:9;
    5737 = 29*197 + 24; hence not 29 divides 5737 by NAT_4:9;
    5737 = 31*185 + 2; hence not 31 divides 5737 by NAT_4:9;
    5737 = 37*155 + 2; hence not 37 divides 5737 by NAT_4:9;
    5737 = 41*139 + 38; hence not 41 divides 5737 by NAT_4:9;
    5737 = 43*133 + 18; hence not 43 divides 5737 by NAT_4:9;
    5737 = 47*122 + 3; hence not 47 divides 5737 by NAT_4:9;
    5737 = 53*108 + 13; hence not 53 divides 5737 by NAT_4:9;
    5737 = 59*97 + 14; hence not 59 divides 5737 by NAT_4:9;
    5737 = 61*94 + 3; hence not 61 divides 5737 by NAT_4:9;
    5737 = 67*85 + 42; hence not 67 divides 5737 by NAT_4:9;
    5737 = 71*80 + 57; hence not 71 divides 5737 by NAT_4:9;
    5737 = 73*78 + 43; hence not 73 divides 5737 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5737 & n is prime
  holds not n divides 5737 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
