
theorem
  5813 is prime
proof
  now
    5813 = 2*2906 + 1; hence not 2 divides 5813 by NAT_4:9;
    5813 = 3*1937 + 2; hence not 3 divides 5813 by NAT_4:9;
    5813 = 5*1162 + 3; hence not 5 divides 5813 by NAT_4:9;
    5813 = 7*830 + 3; hence not 7 divides 5813 by NAT_4:9;
    5813 = 11*528 + 5; hence not 11 divides 5813 by NAT_4:9;
    5813 = 13*447 + 2; hence not 13 divides 5813 by NAT_4:9;
    5813 = 17*341 + 16; hence not 17 divides 5813 by NAT_4:9;
    5813 = 19*305 + 18; hence not 19 divides 5813 by NAT_4:9;
    5813 = 23*252 + 17; hence not 23 divides 5813 by NAT_4:9;
    5813 = 29*200 + 13; hence not 29 divides 5813 by NAT_4:9;
    5813 = 31*187 + 16; hence not 31 divides 5813 by NAT_4:9;
    5813 = 37*157 + 4; hence not 37 divides 5813 by NAT_4:9;
    5813 = 41*141 + 32; hence not 41 divides 5813 by NAT_4:9;
    5813 = 43*135 + 8; hence not 43 divides 5813 by NAT_4:9;
    5813 = 47*123 + 32; hence not 47 divides 5813 by NAT_4:9;
    5813 = 53*109 + 36; hence not 53 divides 5813 by NAT_4:9;
    5813 = 59*98 + 31; hence not 59 divides 5813 by NAT_4:9;
    5813 = 61*95 + 18; hence not 61 divides 5813 by NAT_4:9;
    5813 = 67*86 + 51; hence not 67 divides 5813 by NAT_4:9;
    5813 = 71*81 + 62; hence not 71 divides 5813 by NAT_4:9;
    5813 = 73*79 + 46; hence not 73 divides 5813 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5813 & n is prime
  holds not n divides 5813 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
