
theorem
  3041 is prime
proof
  now
    3041 = 2*1520 + 1; hence not 2 divides 3041 by NAT_4:9;
    3041 = 3*1013 + 2; hence not 3 divides 3041 by NAT_4:9;
    3041 = 5*608 + 1; hence not 5 divides 3041 by NAT_4:9;
    3041 = 7*434 + 3; hence not 7 divides 3041 by NAT_4:9;
    3041 = 11*276 + 5; hence not 11 divides 3041 by NAT_4:9;
    3041 = 13*233 + 12; hence not 13 divides 3041 by NAT_4:9;
    3041 = 17*178 + 15; hence not 17 divides 3041 by NAT_4:9;
    3041 = 19*160 + 1; hence not 19 divides 3041 by NAT_4:9;
    3041 = 23*132 + 5; hence not 23 divides 3041 by NAT_4:9;
    3041 = 29*104 + 25; hence not 29 divides 3041 by NAT_4:9;
    3041 = 31*98 + 3; hence not 31 divides 3041 by NAT_4:9;
    3041 = 37*82 + 7; hence not 37 divides 3041 by NAT_4:9;
    3041 = 41*74 + 7; hence not 41 divides 3041 by NAT_4:9;
    3041 = 43*70 + 31; hence not 43 divides 3041 by NAT_4:9;
    3041 = 47*64 + 33; hence not 47 divides 3041 by NAT_4:9;
    3041 = 53*57 + 20; hence not 53 divides 3041 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3041 & n is prime
  holds not n divides 3041 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
