
theorem
  7027 is prime
proof
  now
    7027 = 2*3513 + 1; hence not 2 divides 7027 by NAT_4:9;
    7027 = 3*2342 + 1; hence not 3 divides 7027 by NAT_4:9;
    7027 = 5*1405 + 2; hence not 5 divides 7027 by NAT_4:9;
    7027 = 7*1003 + 6; hence not 7 divides 7027 by NAT_4:9;
    7027 = 11*638 + 9; hence not 11 divides 7027 by NAT_4:9;
    7027 = 13*540 + 7; hence not 13 divides 7027 by NAT_4:9;
    7027 = 17*413 + 6; hence not 17 divides 7027 by NAT_4:9;
    7027 = 19*369 + 16; hence not 19 divides 7027 by NAT_4:9;
    7027 = 23*305 + 12; hence not 23 divides 7027 by NAT_4:9;
    7027 = 29*242 + 9; hence not 29 divides 7027 by NAT_4:9;
    7027 = 31*226 + 21; hence not 31 divides 7027 by NAT_4:9;
    7027 = 37*189 + 34; hence not 37 divides 7027 by NAT_4:9;
    7027 = 41*171 + 16; hence not 41 divides 7027 by NAT_4:9;
    7027 = 43*163 + 18; hence not 43 divides 7027 by NAT_4:9;
    7027 = 47*149 + 24; hence not 47 divides 7027 by NAT_4:9;
    7027 = 53*132 + 31; hence not 53 divides 7027 by NAT_4:9;
    7027 = 59*119 + 6; hence not 59 divides 7027 by NAT_4:9;
    7027 = 61*115 + 12; hence not 61 divides 7027 by NAT_4:9;
    7027 = 67*104 + 59; hence not 67 divides 7027 by NAT_4:9;
    7027 = 71*98 + 69; hence not 71 divides 7027 by NAT_4:9;
    7027 = 73*96 + 19; hence not 73 divides 7027 by NAT_4:9;
    7027 = 79*88 + 75; hence not 79 divides 7027 by NAT_4:9;
    7027 = 83*84 + 55; hence not 83 divides 7027 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7027 & n is prime
  holds not n divides 7027 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
