
theorem
  3089 is prime
proof
  now
    3089 = 2*1544 + 1; hence not 2 divides 3089 by NAT_4:9;
    3089 = 3*1029 + 2; hence not 3 divides 3089 by NAT_4:9;
    3089 = 5*617 + 4; hence not 5 divides 3089 by NAT_4:9;
    3089 = 7*441 + 2; hence not 7 divides 3089 by NAT_4:9;
    3089 = 11*280 + 9; hence not 11 divides 3089 by NAT_4:9;
    3089 = 13*237 + 8; hence not 13 divides 3089 by NAT_4:9;
    3089 = 17*181 + 12; hence not 17 divides 3089 by NAT_4:9;
    3089 = 19*162 + 11; hence not 19 divides 3089 by NAT_4:9;
    3089 = 23*134 + 7; hence not 23 divides 3089 by NAT_4:9;
    3089 = 29*106 + 15; hence not 29 divides 3089 by NAT_4:9;
    3089 = 31*99 + 20; hence not 31 divides 3089 by NAT_4:9;
    3089 = 37*83 + 18; hence not 37 divides 3089 by NAT_4:9;
    3089 = 41*75 + 14; hence not 41 divides 3089 by NAT_4:9;
    3089 = 43*71 + 36; hence not 43 divides 3089 by NAT_4:9;
    3089 = 47*65 + 34; hence not 47 divides 3089 by NAT_4:9;
    3089 = 53*58 + 15; hence not 53 divides 3089 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3089 & n is prime
  holds not n divides 3089 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
