
theorem
  4091 is prime
proof
  now
    4091 = 2*2045 + 1; hence not 2 divides 4091 by NAT_4:9;
    4091 = 3*1363 + 2; hence not 3 divides 4091 by NAT_4:9;
    4091 = 5*818 + 1; hence not 5 divides 4091 by NAT_4:9;
    4091 = 7*584 + 3; hence not 7 divides 4091 by NAT_4:9;
    4091 = 11*371 + 10; hence not 11 divides 4091 by NAT_4:9;
    4091 = 13*314 + 9; hence not 13 divides 4091 by NAT_4:9;
    4091 = 17*240 + 11; hence not 17 divides 4091 by NAT_4:9;
    4091 = 19*215 + 6; hence not 19 divides 4091 by NAT_4:9;
    4091 = 23*177 + 20; hence not 23 divides 4091 by NAT_4:9;
    4091 = 29*141 + 2; hence not 29 divides 4091 by NAT_4:9;
    4091 = 31*131 + 30; hence not 31 divides 4091 by NAT_4:9;
    4091 = 37*110 + 21; hence not 37 divides 4091 by NAT_4:9;
    4091 = 41*99 + 32; hence not 41 divides 4091 by NAT_4:9;
    4091 = 43*95 + 6; hence not 43 divides 4091 by NAT_4:9;
    4091 = 47*87 + 2; hence not 47 divides 4091 by NAT_4:9;
    4091 = 53*77 + 10; hence not 53 divides 4091 by NAT_4:9;
    4091 = 59*69 + 20; hence not 59 divides 4091 by NAT_4:9;
    4091 = 61*67 + 4; hence not 61 divides 4091 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4091 & n is prime
  holds not n divides 4091 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
