
theorem
  6577 is prime
proof
  now
    6577 = 2*3288 + 1; hence not 2 divides 6577 by NAT_4:9;
    6577 = 3*2192 + 1; hence not 3 divides 6577 by NAT_4:9;
    6577 = 5*1315 + 2; hence not 5 divides 6577 by NAT_4:9;
    6577 = 7*939 + 4; hence not 7 divides 6577 by NAT_4:9;
    6577 = 11*597 + 10; hence not 11 divides 6577 by NAT_4:9;
    6577 = 13*505 + 12; hence not 13 divides 6577 by NAT_4:9;
    6577 = 17*386 + 15; hence not 17 divides 6577 by NAT_4:9;
    6577 = 19*346 + 3; hence not 19 divides 6577 by NAT_4:9;
    6577 = 23*285 + 22; hence not 23 divides 6577 by NAT_4:9;
    6577 = 29*226 + 23; hence not 29 divides 6577 by NAT_4:9;
    6577 = 31*212 + 5; hence not 31 divides 6577 by NAT_4:9;
    6577 = 37*177 + 28; hence not 37 divides 6577 by NAT_4:9;
    6577 = 41*160 + 17; hence not 41 divides 6577 by NAT_4:9;
    6577 = 43*152 + 41; hence not 43 divides 6577 by NAT_4:9;
    6577 = 47*139 + 44; hence not 47 divides 6577 by NAT_4:9;
    6577 = 53*124 + 5; hence not 53 divides 6577 by NAT_4:9;
    6577 = 59*111 + 28; hence not 59 divides 6577 by NAT_4:9;
    6577 = 61*107 + 50; hence not 61 divides 6577 by NAT_4:9;
    6577 = 67*98 + 11; hence not 67 divides 6577 by NAT_4:9;
    6577 = 71*92 + 45; hence not 71 divides 6577 by NAT_4:9;
    6577 = 73*90 + 7; hence not 73 divides 6577 by NAT_4:9;
    6577 = 79*83 + 20; hence not 79 divides 6577 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6577 & n is prime
  holds not n divides 6577 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
