
theorem
  5801 is prime
proof
  now
    5801 = 2*2900 + 1; hence not 2 divides 5801 by NAT_4:9;
    5801 = 3*1933 + 2; hence not 3 divides 5801 by NAT_4:9;
    5801 = 5*1160 + 1; hence not 5 divides 5801 by NAT_4:9;
    5801 = 7*828 + 5; hence not 7 divides 5801 by NAT_4:9;
    5801 = 11*527 + 4; hence not 11 divides 5801 by NAT_4:9;
    5801 = 13*446 + 3; hence not 13 divides 5801 by NAT_4:9;
    5801 = 17*341 + 4; hence not 17 divides 5801 by NAT_4:9;
    5801 = 19*305 + 6; hence not 19 divides 5801 by NAT_4:9;
    5801 = 23*252 + 5; hence not 23 divides 5801 by NAT_4:9;
    5801 = 29*200 + 1; hence not 29 divides 5801 by NAT_4:9;
    5801 = 31*187 + 4; hence not 31 divides 5801 by NAT_4:9;
    5801 = 37*156 + 29; hence not 37 divides 5801 by NAT_4:9;
    5801 = 41*141 + 20; hence not 41 divides 5801 by NAT_4:9;
    5801 = 43*134 + 39; hence not 43 divides 5801 by NAT_4:9;
    5801 = 47*123 + 20; hence not 47 divides 5801 by NAT_4:9;
    5801 = 53*109 + 24; hence not 53 divides 5801 by NAT_4:9;
    5801 = 59*98 + 19; hence not 59 divides 5801 by NAT_4:9;
    5801 = 61*95 + 6; hence not 61 divides 5801 by NAT_4:9;
    5801 = 67*86 + 39; hence not 67 divides 5801 by NAT_4:9;
    5801 = 71*81 + 50; hence not 71 divides 5801 by NAT_4:9;
    5801 = 73*79 + 34; hence not 73 divides 5801 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5801 & n is prime
  holds not n divides 5801 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
