
theorem
  1613 is prime
proof
  now
    1613 = 2*806 + 1; hence not 2 divides 1613 by NAT_4:9;
    1613 = 3*537 + 2; hence not 3 divides 1613 by NAT_4:9;
    1613 = 5*322 + 3; hence not 5 divides 1613 by NAT_4:9;
    1613 = 7*230 + 3; hence not 7 divides 1613 by NAT_4:9;
    1613 = 11*146 + 7; hence not 11 divides 1613 by NAT_4:9;
    1613 = 13*124 + 1; hence not 13 divides 1613 by NAT_4:9;
    1613 = 17*94 + 15; hence not 17 divides 1613 by NAT_4:9;
    1613 = 19*84 + 17; hence not 19 divides 1613 by NAT_4:9;
    1613 = 23*70 + 3; hence not 23 divides 1613 by NAT_4:9;
    1613 = 29*55 + 18; hence not 29 divides 1613 by NAT_4:9;
    1613 = 31*52 + 1; hence not 31 divides 1613 by NAT_4:9;
    1613 = 37*43 + 22; hence not 37 divides 1613 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1613 & n is prime
  holds not n divides 1613 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
