
theorem
  4051 is prime
proof
  now
    4051 = 2*2025 + 1; hence not 2 divides 4051 by NAT_4:9;
    4051 = 3*1350 + 1; hence not 3 divides 4051 by NAT_4:9;
    4051 = 5*810 + 1; hence not 5 divides 4051 by NAT_4:9;
    4051 = 7*578 + 5; hence not 7 divides 4051 by NAT_4:9;
    4051 = 11*368 + 3; hence not 11 divides 4051 by NAT_4:9;
    4051 = 13*311 + 8; hence not 13 divides 4051 by NAT_4:9;
    4051 = 17*238 + 5; hence not 17 divides 4051 by NAT_4:9;
    4051 = 19*213 + 4; hence not 19 divides 4051 by NAT_4:9;
    4051 = 23*176 + 3; hence not 23 divides 4051 by NAT_4:9;
    4051 = 29*139 + 20; hence not 29 divides 4051 by NAT_4:9;
    4051 = 31*130 + 21; hence not 31 divides 4051 by NAT_4:9;
    4051 = 37*109 + 18; hence not 37 divides 4051 by NAT_4:9;
    4051 = 41*98 + 33; hence not 41 divides 4051 by NAT_4:9;
    4051 = 43*94 + 9; hence not 43 divides 4051 by NAT_4:9;
    4051 = 47*86 + 9; hence not 47 divides 4051 by NAT_4:9;
    4051 = 53*76 + 23; hence not 53 divides 4051 by NAT_4:9;
    4051 = 59*68 + 39; hence not 59 divides 4051 by NAT_4:9;
    4051 = 61*66 + 25; hence not 61 divides 4051 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4051 & n is prime
  holds not n divides 4051 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
