
theorem
  3613 is prime
proof
  now
    3613 = 2*1806 + 1; hence not 2 divides 3613 by NAT_4:9;
    3613 = 3*1204 + 1; hence not 3 divides 3613 by NAT_4:9;
    3613 = 5*722 + 3; hence not 5 divides 3613 by NAT_4:9;
    3613 = 7*516 + 1; hence not 7 divides 3613 by NAT_4:9;
    3613 = 11*328 + 5; hence not 11 divides 3613 by NAT_4:9;
    3613 = 13*277 + 12; hence not 13 divides 3613 by NAT_4:9;
    3613 = 17*212 + 9; hence not 17 divides 3613 by NAT_4:9;
    3613 = 19*190 + 3; hence not 19 divides 3613 by NAT_4:9;
    3613 = 23*157 + 2; hence not 23 divides 3613 by NAT_4:9;
    3613 = 29*124 + 17; hence not 29 divides 3613 by NAT_4:9;
    3613 = 31*116 + 17; hence not 31 divides 3613 by NAT_4:9;
    3613 = 37*97 + 24; hence not 37 divides 3613 by NAT_4:9;
    3613 = 41*88 + 5; hence not 41 divides 3613 by NAT_4:9;
    3613 = 43*84 + 1; hence not 43 divides 3613 by NAT_4:9;
    3613 = 47*76 + 41; hence not 47 divides 3613 by NAT_4:9;
    3613 = 53*68 + 9; hence not 53 divides 3613 by NAT_4:9;
    3613 = 59*61 + 14; hence not 59 divides 3613 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3613 & n is prime
  holds not n divides 3613 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
