
theorem
  2591 is prime
proof
  now
    2591 = 2*1295 + 1; hence not 2 divides 2591 by NAT_4:9;
    2591 = 3*863 + 2; hence not 3 divides 2591 by NAT_4:9;
    2591 = 5*518 + 1; hence not 5 divides 2591 by NAT_4:9;
    2591 = 7*370 + 1; hence not 7 divides 2591 by NAT_4:9;
    2591 = 11*235 + 6; hence not 11 divides 2591 by NAT_4:9;
    2591 = 13*199 + 4; hence not 13 divides 2591 by NAT_4:9;
    2591 = 17*152 + 7; hence not 17 divides 2591 by NAT_4:9;
    2591 = 19*136 + 7; hence not 19 divides 2591 by NAT_4:9;
    2591 = 23*112 + 15; hence not 23 divides 2591 by NAT_4:9;
    2591 = 29*89 + 10; hence not 29 divides 2591 by NAT_4:9;
    2591 = 31*83 + 18; hence not 31 divides 2591 by NAT_4:9;
    2591 = 37*70 + 1; hence not 37 divides 2591 by NAT_4:9;
    2591 = 41*63 + 8; hence not 41 divides 2591 by NAT_4:9;
    2591 = 43*60 + 11; hence not 43 divides 2591 by NAT_4:9;
    2591 = 47*55 + 6; hence not 47 divides 2591 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2591 & n is prime
  holds not n divides 2591 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
